1. Find the rule which gives the number of matchsticks required to make the following matchsticks patterns. Use a variable to write the rule.
(a) A pattern of letter T as
(b) A pattern of letter Z as
(c) A pattern of letter U as
(d) A pattern of letter V as
(e) A pattern of letter E as
(f) A pattern of letter S as
(g) A pattern of letter A as
1. Find the rule which gives the number of matchsticks required to make the following matchsticks patterns. Use a variable to write the rule.
(a) A pattern of letter T as
(b) A pattern of letter Z as
(c) A pattern of letter U as
(d) A pattern of letter V as
(e) A pattern of letter E as
(f) A pattern of letter S as
(g) A pattern of letter A as
Explanation:
(a)
Matchsticks that are needed to form a single letter T is 2. So, to make a pattern number of matchstick required is 2x.
(b)
Matchsticks that are needed to form a single letter Z is 3. So, to make a pattern number of matchstick required is 3x.
(c)
Matchsticks that are needed to form a single letter U is 3. So, to make a pattern number of matchstick required is 3x.
(d)
Matchsticks that are needed to form a single letter V is 2. So, to make a pattern number of matchstick required is 2x.
(e)
Matchsticks that are needed to form a single letter E is 5. So, to make a pattern number of matchstick required is 5x.
(f)
Matchsticks that are needed to form a single letter S is 5. So, to make a pattern number of matchstick required is 5x.
(g)
Matchsticks that are needed to form a single letter A is 6. So, to make a pattern number of matchstick required is 6x.
2. We already know the rule for the pattern of letters L, C and F. Some of the letters from Q.1 (given above) give us the same rule as that given by L. Which are these? Why does this happen?
2. We already know the rule for the pattern of letters L, C and F. Some of the letters from Q.1 (given above) give us the same rule as that given by L. Which are these? Why does this happen?
Explanation:
Matchsticks that are needed to form a single letter L is 2. The letters T and V also require only 2 matchsticks. So, answer is option (a) and (d).
3. Cadets are marching in a parade. There are 5 cadets in a row. What is the rule which gives the number of cadets, given the number of rows? (Use n for the number of rows)
3. Cadets are marching in a parade. There are 5 cadets in a row. What is the rule which gives the number of cadets, given the number of rows? (Use n for the number of rows)
Explanation:
Assuming there are n rows present.
One row has 5 cadets.
Two rows would have = 2×5 = 10 cadets.
Three rows would have = 3×5 = 15 cadets.
So, n rows would have = n×5 = 5n cadets.
4. If there are 50 mangoes in a box, how will you write the total number of mangoes in terms of the number of boxes? (Use b for the number of boxes.)
4. If there are 50 mangoes in a box, how will you write the total number of mangoes in terms of the number of boxes? (Use b for the number of boxes.)
Explanation:
Assuming there are b boxes present.
One box has 50 mangoes.
Two boxes would have = 2×50 = 100 mangoes.
Three boxes would have = 3×50 = 150 mangoes.
So, b boxes would have = b×50 = 50b mangoes.
5. The teacher distributes 5 pencils per students. Can you tell how many pencils are needed, given the number of students? (Use s for the number of students.)
5. The teacher distributes 5 pencils per students. Can you tell how many pencils are needed, given the number of students? (Use s for the number of students.)
Explanation:
Assuming there are s student present.
One student gets 5 pencils.
Two students would get = 2×5 = 10 pencils.
Three students would get = 3×5 = 15 pencils.
So, s students would get = s×50 = 50s pencils.
6. A bird flies 1 kilometer in one minute. Can you express the distance covered by the birds in terms of its flying time in minutes? (Use t for flying time in minutes.)
6. A bird flies 1 kilometer in one minute. Can you express the distance covered by the birds in terms of its flying time in minutes? (Use t for flying time in minutes.)
Explanation:
Assuming time taken to fly is t minute.
In one minute of time, distance that is covered = 1 km.
In two minute of time, distance that is covered = 2 km.
So, in t minute of time, distance that is covered = t km.
7. Radha is drawing a dot Rangoli (a beautiful pattern of lines joining dots) with chalk powder. She has 9 dots in a row. How many dots will her Rangoli have for r rows? How many dots are there if there are 8 rows? If there are 10 rows?
7. Radha is drawing a dot Rangoli (a beautiful pattern of lines joining dots) with chalk powder. She has 9 dots in a row. How many dots will her Rangoli have for r rows? How many dots are there if there are 8 rows? If there are 10 rows?
Explanation:
Dots that are present in one row = 9
If there are r rows present,
In r rows, number of dots would be = Dots present in one row × total rows present
= 9×r = 9r
Dots present in 8 rows = 9×8 = 72
Dots present in 10 rows = 9×10 = 90
8. Leela is Radha’s younger sister. Leela is 4 years younger than Radha. Can you write Leela’s age in terms of Radha’s age? Take Radha’s age to be x years.
8. Leela is Radha’s younger sister. Leela is 4 years younger than Radha. Can you write Leela’s age in terms of Radha’s age? Take Radha’s age to be x years.
Explanation:
Age that Radha is given to be x years.
Age of Leela = 4 years less than that of Radha age
Age of Leela = (x – 4) years
9. Mother has made laddus. She gives some laddus to guests and family members; still 5 laddus remain. If the number of laddus mother gave away is l, how many laddus did she make?
9. Mother has made laddus. She gives some laddus to guests and family members; still 5 laddus remain. If the number of laddus mother gave away is l, how many laddus did she make?
Explanation:
Laddus that were given away by mother = l
Laddus that are left = 5
Total laddus made by mother = Laddus that are left + Laddus that mother gave away
= (5 + 1) laddus
= 6 laddus
10. Oranges are to be transferred from larger boxes into smaller boxes. When a large box is emptied, the oranges from it fill two smaller boxes and still 10 oranges remain outside. If the number of oranges in a small box are taken to be x, what is the number of oranges in the larger box?
10. Oranges are to be transferred from larger boxes into smaller boxes. When a large box is emptied, the oranges from it fill two smaller boxes and still 10 oranges remain outside. If the number of oranges in a small box are taken to be x, what is the number of oranges in the larger box?
Explanation:
One small box contains oranges = x
Two small box contains oranges = 2x
Oranges remained outside = 10
Large box contains oranges = Two small boxes contains oranges + Oranges remained outside
= 2x + 10
11. (a) Look at the following matchstick pattern of squares (Fig 11.6). The squares are not separate. Two neighbouring squares have a common matchstick. Observe the patterns and find the rule that gives the number of matchsticks
in terms of the number of squares. (Hint: If you remove vertical stick at the end, you will get a pattern of Cs)
(b) Fig 11.7 gives a matchstick pattern of triangles. As in Exercise 11 (a) above, find the general rule that gives the number of matchsticks in terms of the number of triangles.
11. (a) Look at the following matchstick pattern of squares (Fig 11.6). The squares are not separate. Two neighbouring squares have a common matchstick. Observe the patterns and find the rule that gives the number of matchsticks
in terms of the number of squares. (Hint: If you remove vertical stick at the end, you will get a pattern of Cs)
(b) Fig 11.7 gives a matchstick pattern of triangles. As in Exercise 11 (a) above, find the general rule that gives the number of matchsticks in terms of the number of triangles.
Explanation:
(a) In the given pattern figure (a) has 4 matchsticks, figure (b) has 7 matchsticks, figure (c) has 10 matchsticks and figure (d) has 10 matchsticks. So, next figure would have 13 matchsticks. The pattern contains 1 more than 3 times the number of squares present in the pattern.
So, every pattern has 3x + 1 matchsticks, here x is number of squares present in that pattern.
(b) In the given pattern figure (a) has 3 matchsticks, figure (b) has 5 matchsticks, figure (c) has 7 matchsticks and figure (d) has 9 matchsticks. So, next figure would have 11 matchsticks. The pattern contains 1 more than 2 times the number of triangles present in the pattern.
So, every pattern has 2x + 1 matchsticks, here x is number of triangles present in that pattern.
12. The side of an equilateral triangle is shown by l. Express the perimeter of the equilateral triangle using l.
12. The side of an equilateral triangle is shown by l. Express the perimeter of the equilateral triangle using l.
Explanation:
Side length of equilateral triangle = l
The equilateral triangle contains three sides of equal length. So, perimeter is sum of all sides
Perimeter of the equilateral triangle = 3 × l = 3l
13. The side of the regular hexagon (Fig 11.10) is denoted by l. Express the perimeter of the hexagon using l.
(Hint: A regular hexagon has all its six sides equal in length.)
13. The side of the regular hexagon (Fig 11.10) is denoted by l. Express the perimeter of the hexagon using l.
(Hint: A regular hexagon has all its six sides equal in length.)
Explanation:
Side length of a regular hexagon is = l
The hexagon contains six sides of equal length. So, perimeter is sum of all sides
Perimeter of the hexagon = 6 × l = 6l
14. A cube is a three-dimensional figure as shown in Fig 11.11. It has six faces and all of them are identical squares. The length of an edge of the cube is given by l. Find the formula for the total length of the edges of a cube.
14. A cube is a three-dimensional figure as shown in Fig 11.11. It has six faces and all of them are identical squares. The length of an edge of the cube is given by l. Find the formula for the total length of the edges of a cube.
Explanation:
Cube has an edge length = l
Number of edges that a cube has = 12
Length of total edges that cube has = Cube’s edge length × Number of edges that a cube has
= l × 12
= 12l
15. The diameter of a circle is a line which joins two points on the circle and also passes through the centre of the circle. (In the adjoining figure (Fig 11.2) AB is a diameter of a circle; C is its centre.) Express the diameter of the circle (d) in terms of its radius (r).
15. The diameter of a circle is a line which joins two points on the circle and also passes through the centre of the circle. (In the adjoining figure (Fig 11.2) AB is a diameter of a circle; C is its centre.) Express the diameter of the circle (d) in terms of its radius (r).
Explanation:
It has been given that,
AC = CB = CP = r
Circle’s diameter = AB
= AC + CB
= r + r
= 2r
So, in a circle diameter is 2 times the radius.
16. To find sum of three numbers 14, 27 and 13 we can have two ways:
(a) We may first add 14 and 27 to get 41 and then add 13 to it to get the total sum 54 or
(b) We may add 27 and 13 to get 40 and then add 14 to get the sum 54. Thus, (14 + 27) + 13 = 14 + (27 + 13)
16. To find sum of three numbers 14, 27 and 13 we can have two ways:
(a) We may first add 14 and 27 to get 41 and then add 13 to it to get the total sum 54 or
(b) We may add 27 and 13 to get 40 and then add 14 to get the sum 54. Thus, (14 + 27) + 13 = 14 + (27 + 13)
Explanation:
Possible for any three numbers. The property is called the associativity of addition of numbers.
Given numbers are a, b and c then we can write
(a + b) + c = a + (b + c)
17. Make up as many expressions with numbers (no variables) as you can from three numbers 5, 7 and 8. Every number should be used not more than once. Use only addition, subtraction and multiplication.
17. Make up as many expressions with numbers (no variables) as you can from three numbers 5, 7 and 8. Every number should be used not more than once. Use only addition, subtraction and multiplication.
Explanation:
Expressions made by 5, 7 and 8 are given
7 × (5 + 8)
7 × (8 – 5)
(8 – 7) × 5
(7 + 8) × 5
8 × (5 + 7)
8 × (7 – 5)
18. Which out of the following are expressions with numbers only?
(a) y + 3
(b) (7 × 20) – 8z
(c) 5 (21 – 7) + 7 × 2
(d) 5
(e) 3x
(f) 5 – 5n
(g) (7 × 20) – (5 × 10) – 45 + p
18. Which out of the following are expressions with numbers only?
(a) y + 3
(b) (7 × 20) – 8z
(c) 5 (21 – 7) + 7 × 2
(d) 5
(e) 3x
(f) 5 – 5n
(g) (7 × 20) – (5 × 10) – 45 + p
Explanation:
The expressions that contain only numbers are option- (c) and (d).
19. Identify the operations (addition, subtraction, division, multiplication) in forming the following expressions and tell how the expressions have been formed.
(a) z + 1, z – 1, y + 17, y – 17
(b) 17y, y / 17, 5z
(c) 2y + 17, 2y – 17
(d) 7m, –7m + 3, –7m – 3
19. Identify the operations (addition, subtraction, division, multiplication) in forming the following expressions and tell how the expressions have been formed.
(a) z + 1, z – 1, y + 17, y – 17
(b) 17y, y / 17, 5z
(c) 2y + 17, 2y – 17
(d) 7m, –7m + 3, –7m – 3
Explanation:
(a)
⇨ Addition, z + 1 is formed by adding 1 with z
⇨ Subtraction, z – 1 is formed by subtracting 1 with z
⇨ Addition, y + 17 is formed by adding 17 with y
⇨ Subtraction, y – 17 is formed by subtracting 17 with y
(b)
⇨ Multiplication, 17y is formed by multiplying 17 with y
⇨ Division, y/17 is formed by dividing 17 with y
⇨ Multiplication, 5z is formed by multiplying 5 with z
(c)
⇨ Multiply then add, multiply 2 with y then 17 is added.
⇨ Multiply and subtract, multiply 2 with y then 17 is subtracted
(d)
⇨ Multiply, multiply m with 7.
⇨ Multiply and add, –7 is multiply with m then added with 3
⇨ Multiply and subtract, –7 is multiply with m then subtracted with 3.
20. Give expressions for the following cases.
(a) 7 added to p
(b) 7 subtracted from p
(c) p multiplied by 7
(d) p divided by 7
(e) 7 subtracted from –m
(f) –p multiplied by 5
(g) –p divided by 5
(h) p multiplied by -5
20. Give expressions for the following cases.
(a) 7 added to p
(b) 7 subtracted from p
(c) p multiplied by 7
(d) p divided by 7
(e) 7 subtracted from –m
(f) –p multiplied by 5
(g) –p divided by 5
(h) p multiplied by -5
Explanation:
(a) Add 7 with p ⇨ (p+7)
(b) Subtract 7 with p ⇨ (p–7)
(c) Multiply 7 with p ⇨ (7p)
(d) Divide 7 with p ⇨ (p / 7)
(e) Subtract –7 with –m, ⇨ (–m – 7)
(f) Multiply 5 with –p ⇨ (–5p)
(g) Divide 5 with –p ⇨ (–p / 5)
(h) Multiply –5 with p ⇨ (–5p)
21. Give expressions in the following cases.
(a) 11 added to 2m
(b) 11 subtracted from 2m
(c) 5 times y to which 3 is added
(d) 5 times y from which 3 is subtracted
(e) y is multiplied by -8
(f) y is multiplied by -8 and then 5 is added to the result
(g) y is multiplied by 5 and the result is subtracted from 16
(h) y is multiplied by -5 and the result is added to 16.
21. Give expressions in the following cases.
(a) 11 added to 2m
(b) 11 subtracted from 2m
(c) 5 times y to which 3 is added
(d) 5 times y from which 3 is subtracted
(e) y is multiplied by -8
(f) y is multiplied by -8 and then 5 is added to the result
(g) y is multiplied by 5 and the result is subtracted from 16
(h) y is multiplied by -5 and the result is added to 16.
Explanation:
(a) Add 11 with 2m ⇨ (2m + 11)
(b) Subtract 11 with 2m ⇨ (2m – 11)
(c) Multiply 5 with y then add with 3 ⇨ (5y + 3)
(d) Multiply 5 with y then subtract with 3 ⇨ (5y – 3)
(e) Multiply y with –8 ⇨ (–8y)
(f) Multiply y with –8 then add with 5 ⇨ (–8y + 5)
(g) Multiply y with 5 then subtract from 16 ⇨ (16 – 5y)
(h) Multiply y with –5 then add with 16 ⇨ (–5y + 16)
22. (a) Form expressions using t and 4. Use not more than one number operation. Every expression must have t in it.
(b) Form expressions using y, 2 and 7. Every expression must have y in it. Use only two number operations. These should be different.
22. (a) Form expressions using t and 4. Use not more than one number operation. Every expression must have t in it.
(b) Form expressions using y, 2 and 7. Every expression must have y in it. Use only two number operations. These should be different.
Explanation:
(a) Some of the equations are- (4 – t), (4/t), (t/4), (4t), (4 + t), (t – 4), (t + 4)
(b) Some of the equations are- 7y + 2, 2y + 7, 7y – 2, 2y – 7
23. Answer the following:
(a) Take Sarita’s present age to be y years
(i) What will be her age 5 years from now?
(ii) What was her age 3 years back?
(iii) Sarita’s grandfather is 6 times her age. What is the age of her grandfather?
(iv) Grandmother is two year younger than grandfather. What is grandmother’s age?
(v) Sarita’s father’s age is 5 years more than 3 times Sarita’s age. What is her father’s age?
(b) The length of a rectangular hall is 4 meters less than three times the breadth of the hall. What is the length, if the breadth is b meters?
(c) A rectangular box has height h cm. Its length is 5 times the height and breadth is 10 cm less than the length. Express the length and the breadth of the box in terms of the height.
(d) Meena, Beena and Reena are climbing the steps to the hill top. Meena is at step s, Beena is 8 steps ahead and Leena 7 steps behind. Where are Beena and Meena? The total number of steps to the hill top is 10 less than 4 times what Meena has reached. Express the total number of steps using s.
(e) A bus travels at v km per hour. It is going from Daspur to Beespur. After the bus has travelled 5 hours, Beespur is still 20 km away. What is the distance from Daspur to Beespur? Express it using v.
23. Answer the following:
(a) Take Sarita’s present age to be y years
(i) What will be her age 5 years from now?
(ii) What was her age 3 years back?
(iii) Sarita’s grandfather is 6 times her age. What is the age of her grandfather?
(iv) Grandmother is two year younger than grandfather. What is grandmother’s age?
(v) Sarita’s father’s age is 5 years more than 3 times Sarita’s age. What is her father’s age?
(b) The length of a rectangular hall is 4 meters less than three times the breadth of the hall. What is the length, if the breadth is b meters?
(c) A rectangular box has height h cm. Its length is 5 times the height and breadth is 10 cm less than the length. Express the length and the breadth of the box in terms of the height.
(d) Meena, Beena and Reena are climbing the steps to the hill top. Meena is at step s, Beena is 8 steps ahead and Leena 7 steps behind. Where are Beena and Meena? The total number of steps to the hill top is 10 less than 4 times what Meena has reached. Express the total number of steps using s.
(e) A bus travels at v km per hour. It is going from Daspur to Beespur. After the bus has travelled 5 hours, Beespur is still 20 km away. What is the distance from Daspur to Beespur? Express it using v.
Explanation:
(a)
(i) 5 years later Sarita age will be = Her current age + 5
= (y + 5) years
(ii) 3 years before Sarita age would have been = Her current age – 3
= (y – 3) years
(iii) Her Grandfather current age = 6× Sarita current age
= 6y years
(iv) Her Grandmother current age = Her Grandfather current age – 2
= (6y – 2) years
(v) Her Father current age = 3 × Sarita’s current age + 5
= (3y + 5) years
(b) hall breadth = b metres
hall length = 3 × hall breadth – 4
⇨ Length of hall = (3b – 4) metres
(c) Height of hall = h cm
Hall length = 5 × hall height
⇨ l = 5h cm
Hall breadth = hall length – 10
⇨ b = (l – 10) cm
⇨ b = (5h – 10) cm
(d) Current step of Meena is = s
⇨ Current step of Beena is = (Current step of Meena) + 8
= (s + 8)
⇨ Current step of Leena is = (Current step of Meena) – 7
= (s – 7)
⇨ steps to get to the hill top = 4 × (Current step of Meena) – 10
= (4s – 10)
(e) bus speed = v km/hr
So, distance covered in 5 hours at speed of v = 5 × v
= 5v km
Length between Daspur and Beespur = Distance covered + Distance remained to cover
= (5v + 20) km
24. Change the following statements using expressions into statements in ordinary language.
(For example, Given Salim scores r runs in a cricket match, Nalin scores (r + 15) runs. In ordinary language – Nalin scores 15 runs more than Salim.)
(a) A notebook costs ₹ p. A book costs ₹ 3p
(b) Tony put q marbles on the table. He has 8 q marbles in his box.
(c) Our class has n students. The school has 20 n students.
(d) Jaggu is z years old. His uncle is 4z years old and his aunt is (4z – 3) years old.
(e) In an arrangement of dots there are r rows. Each row contains 5 dots
24. Change the following statements using expressions into statements in ordinary language.
(For example, Given Salim scores r runs in a cricket match, Nalin scores (r + 15) runs. In ordinary language – Nalin scores 15 runs more than Salim.)
(a) A notebook costs ₹ p. A book costs ₹ 3p
(b) Tony put q marbles on the table. He has 8 q marbles in his box.
(c) Our class has n students. The school has 20 n students.
(d) Jaggu is z years old. His uncle is 4z years old and his aunt is (4z – 3) years old.
(e) In an arrangement of dots there are r rows. Each row contains 5 dots
Explanation:
(a) a notebook cost 3 times more than the book
(b) Box of Tony has 8 times more the number of marbel that is present on the table.
(c) Students present in school is 20 times than students present in a class.
(d) Age that Jaggu uncle is 4 times more than the age of Jaggu and his aunt current age is 3 less than the age that his uncle is.
(e) Dots present is 5 times the rows present.
25. (a) Given Munnu’s age to be x years, can you guess what (x – 2) may show?
Can you guess what (x + 4) may show? What (3x + 7) may show?
(b) Given Sara’s age today to be y years. Think of her age in the future or in the past.
What will the following expression indicate? y + 7, y – 3, y + 4 12 , y – 2 12 .
(c) Given n students in the class like football, what may 2n shows? What may n / 2 show?
25. (a) Given Munnu’s age to be x years, can you guess what (x – 2) may show?
Can you guess what (x + 4) may show? What (3x + 7) may show?
(b) Given Sara’s age today to be y years. Think of her age in the future or in the past.
What will the following expression indicate? y + 7, y – 3, y + 4 12 , y – 2 12 .
(c) Given n students in the class like football, what may 2n shows? What may n / 2 show?
Explanation:
(a) (x – 2) is age of person who is 2 years younger than the age of Munnu.
(x + 4) is age of person who is 4 years older than the age of Munnu.
(3x + 7) is age of person who is 7 years older than 3 times present age of Munnu.
(b) (y + 7) is the age of person who is 7 years older than the age of Sara.
(y – 3) is the age of person who is 3 years younger than the age of Sara.
y + 4 12 is the age of person who is 4 12 years older than the age of Sara.
y – 2 12 the age of person who is 2 12 years younger than the age of Sara.
(c) 2n may show the number of students those like to play football and other sports.
n/2 may show the number of students those don’t like to play football.
26. State which of the following are equations (with a variable). Give reason for your answer. Identify the variable from the equations with a variable.
(a) 17 = x + 17
(b) (t – 7) > 5
(c) 4 / 2 = 2
(d) (7 × 3) – 19 = 8
(e) 5 × 4 – 8 = 2x
(f) x – 2 = 0
(g) 2m < 30
(h) 2n + 1 = 11
(i) 7 = (11 × 5) – (12 × 4)
(j) 7 = (11 × 2) + p
(k) 20 = 5y
(l) 3q/ 2 < 5
(m) z + 12 > 24
(n) 20 – (10 – 5) = 3 × 5
(o) 7 – x = 5
26. State which of the following are equations (with a variable). Give reason for your answer. Identify the variable from the equations with a variable.
(a) 17 = x + 17
(b) (t – 7) > 5
(c) 4 / 2 = 2
(d) (7 × 3) – 19 = 8
(e) 5 × 4 – 8 = 2x
(f) x – 2 = 0
(g) 2m < 30
(h) 2n + 1 = 11
(i) 7 = (11 × 5) – (12 × 4)
(j) 7 = (11 × 2) + p
(k) 20 = 5y
(l) 3q/ 2 < 5
(m) z + 12 > 24
(n) 20 – (10 – 5) = 3 × 5
(o) 7 – x = 5
Explanation:
(a) x is variable in the equation
(b) Inequality
(c) No variable in this equation
(d) No variable in this equation
(e) x is variable in the equation
(f) x is variable in the equation
(g) Inequality
(h) n is variable in the equation
(i) No variable in this equation
(j) p is variable in the equation
(k) y is variable in the equation
(l) Inequality
(m) Inequality
(n) No variable in this equation
(o) x is variable in the equation
27. Complete the entries in the third column of the table.
27. Complete the entries in the third column of the table.
Explanation:
(a) No
If, y = 10
LHS = 10y = 10 × 10 = 100, RHS = 80
LHS ≠ RHS
(b) Yes
If, y = 8
LHS = 10y = 10 × 8 = 80, RHS = 80
LHS = RHS
(c) No
If, y = 5
LHS = 10×y = 10 × 5 = 50, RHS = 80
LHS ≠ RHS
(d) No
If, l = 20
LHS = 4×l = 4 × 20 = 80, RHS = 20
LHS ≠ RHS
(e) No
If, l = 80
LHS = 4×l = 4 × 80 = 320, RHS = 20
LHS ≠ RHS
(f) Yes
If, l = 5
LHS = 4×l = 4 × 5 = 20, RHS = 20
LHS = RHS
(g) No
If, b = 5
LHS = b + 5 = 5 + 5 = 10, RHS = 9
LHS ≠ RHS
(h) No
If, b = 9
LHS = b + 9 = 5 + 9 = 14, RHS = 9
LHS ≠ RHS
(i) Yes
If, b = 4
LHS = b + 5 = 4 + 5 = 9, RHS = 9
LHS = RHS
(j) Yes
If, h = 13
LHS = h – 8 = 13 – 8 = 5, RHS = 5
LHS = RHS
(k) No
If, h = 8
LHS = h – 8 = 8 – 8 = 0, RHS = 5
LHS ≠ RHS
(l) No
If, h = 0
LHS = h – 8 = 0– 8 = –8, RHS = 5
LHS ≠ RHS
(m) No
If, p = 3
LHS = p + 3 = 3 + 3 = 6, RHS = 1
LHS ≠ RHS
(n) No
If, p = 1
LHS = p + 3 = 1 + 3 = 4, RHS = 1
LHS ≠ RHS
(o) No
If, p = 0
LHS = p + 3 = 0 + 3 = 3, RHS = 1
LHS ≠ RHS
(p) No
If, p = –1
LHS = p + 3 = –1 + 3 = 2, RHS = 1
LHS ≠ RHS
(q) Yes
If, p = –2
LHS = p + 3 = –2 + 3 = 1, RHS = 1
LHS = RHS
28. Pick out the solution from the values given in the bracket next to each equation.
Show that the other values do not satisfy the equation.
(a) 5m = 60 (10, 5, 12, 15)
(b) n + 12 = 20 (12, 8, 20, 0)
(c) p – 5 = 5 (0, 10, 5 – 5)
(d) q / 2 = 7 (7, 2, 10, 14)
(e) r – 4 = 0 (4, -4, 8, 0)
(f) x + 4 = 2 (-2, 0, 2, 4)
28. Pick out the solution from the values given in the bracket next to each equation.
Show that the other values do not satisfy the equation.
(a) 5m = 60 (10, 5, 12, 15)
(b) n + 12 = 20 (12, 8, 20, 0)
(c) p – 5 = 5 (0, 10, 5 – 5)
(d) q / 2 = 7 (7, 2, 10, 14)
(e) r – 4 = 0 (4, -4, 8, 0)
(f) x + 4 = 2 (-2, 0, 2, 4)
Explanation:
(a) 5m = 60
⇨ If, m = 12
⇨ LHS = 5×12 = 60
⇨ RHS = 60
LHS = RHS
⇨ If, m = 10
⇨ LHS = 5×10 = 50
⇨ RHS = 60
LHS ≠ RHS
⇨ If, m = 5
⇨ LHS = 5×5 = 25
⇨ RHS = 60
LHS ≠ RHS
⇨ If, m = 15
⇨ LHS = 15×5 = 75
⇨ RHS = 60
LHS ≠ RHS
(b) n + 12 = 20
⇨ If, n = 12
⇨ LHS = 12 + 12 = 24
⇨ RHS = 20
LHS ≠ RHS
⇨ If, n = 8
⇨ LHS = 12 + 8 = 20
⇨ RHS = 20
LHS = RHS
⇨ If, n = 20
⇨ LHS = 12 + 20 = 32
⇨ RHS = 20
LHS ≠ RHS
⇨ If, n = 0
⇨ LHS = 12 + 0 = 12
⇨ RHS = 20
LHS ≠ RHS
(c) p – 5 = 5
⇨ If, p = –5
⇨ LHS = –5 – 5 = –10
⇨ RHS = 5
LHS ≠ RHS (not verified)
⇨ If, p = 10
⇨ LHS = 10 – 5 = 5
⇨ RHS = 5
LHS = RHS
⇨ If, p = 5
⇨ LHS = 5 – 5 = 0
⇨ RHS = 5
LHS ≠ RHS (not verified)
⇨ If, p = 0
⇨ LHS = 0 – 5 = –5
⇨ RHS = 5
LHS ≠ RHS (not verified)
(d) q / 2 = 7
⇨ If, q = 2
⇨ LHS = 2/2 = 1
⇨ RHS = 7
LHS ≠ RHS (not verified)
⇨ If, q = 10
⇨ LHS = 10/2 = 5
⇨ RHS = 7
LHS ≠ RHS (not verified)
⇨ If, q = 14
⇨ LHS = 14/2 = 7
⇨ RHS = 7
LHS = RHS
⇨ If, q = 7
⇨ LHS = 7/2 = 3.5
⇨ RHS = 7
LHS ≠ RHS (not verified)
(e) r – 4 = 0
⇨ If, r = 0
⇨ LHS = 0 – 4 = –4
⇨ RHS = 0
LHS ≠ RHS (not verified)
⇨ If, r = 8
⇨ LHS = 8 – 4 = 4
⇨ RHS = 0
LHS ≠ RHS (not verified)
⇨ If, r = 4
⇨ LHS = 4 – 4 = 0
⇨ RHS = 0
LHS = RHS
⇨ If, r = –4
⇨ LHS = –4 – 4 = –8
⇨ RHS = 0
LHS ≠ RHS (not verified)
(f) x + 4 = 2
⇨ If, x = –2
⇨ LHS = –2 + 4 = 2
⇨ RHS = 2
LHS = RHS
⇨ If, x = 4
⇨ LHS = 4 + 4 = 8
⇨ RHS = 2
LHS ≠ RHS (not verified)
⇨ If, x = 0
⇨ LHS = 0 + 4 = 4
⇨ RHS = 2
LHS ≠ RHS (not verified)
⇨ If, x = 2
⇨ LHS = 2 + 4 = 6
⇨ RHS = 2
LHS ≠ RHS (not verified)
29. (a)Complete the table and by inspection of the table find the solution to the equation m + 10 = 16.
(b) Complete the table and by inspection of the table, find the solution to the equation 5t = 35
(c) Complete the table and find the solution of the equation z / 3 = 4 using the table.
(d) Complete the table and find the solution to the equation m – 7 = 3.
29. (a)Complete the table and by inspection of the table find the solution to the equation m + 10 = 16.
(b) Complete the table and by inspection of the table, find the solution to the equation 5t = 35
(c) Complete the table and find the solution of the equation z / 3 = 4 using the table.
(d) Complete the table and find the solution to the equation m – 7 = 3.
Explanation:
(a) m + 10
m = 1, ⇨ 1+10=11
m = 2, ⇨ 2+10=12
m=3, ⇨ 3+10=13
m=4, ⇨ 4+10=14
m=5, ⇨ 5+10=15
m=6, ⇨ 6+10=16
m=7, ⇨ 7+10=17
m=8, ⇨ 8+10=18
m=9, ⇨ 9+10=19
m=10, ⇨ 10+10=20
m=6 satisfies the below relation
m + 10 = 6 + 10 = 16
(b) 5t
t=3, ⇨ 5×3=15
t=4, ⇨ 5×4=20
t=5, ⇨ 5×5=25
t=6, ⇨ 5×6=30
t=7, ⇨ 5×7=35
t=8, ⇨ 5×8=40
t=9, ⇨ 5×9=45
t=10, ⇨ 5×10=50
t=11, ⇨ 5×11=55
t=7 satisfies the below relation
5t = 5 × 7 = 35
(c) z / 3
z=8, ⇨ 8/3=223
z=9, ⇨ 9/3=3
z=10, ⇨ 10/3=313
z=11, ⇨ 11/3=323
z=12, ⇨ 12/3=4
z=13, ⇨ 13/3=413
z=14, ⇨ 14/3=423
z=15, ⇨ 15/3=5
z=16, ⇨ 16/3=513
z = 12 satisfies the below relation
z / 3 = 12 / 3 = 4
(d) m – 7
⇨ m = 13, ⇨ 13–7=6
⇨ m = 12, ⇨ 12–7=5
⇨ m = 11, ⇨ 11–7=4
⇨ m = 10, ⇨ 10–7=3
⇨ m = 9, ⇨ 9–7=2
⇨ m = 8, ⇨ 8–7=1
⇨ m = 7, ⇨ 7–7=0
⇨ m = 6, ⇨ 6–7=–1
⇨ m = 5, ⇨ 5–7=–2
⇨ m = 10 satisfies the below relation
⇨ m – 7 = 10 – 7 = 3
30. Solve the following riddles, you may yourself construct such riddles.
Who am I?
(i) Go round a square
Counting every corner
Thrice and no more!
Add the count to me
To get exactly thirty four!
(ii) For each day of the week
Make an upcount from me
If you make no mistake
You will get twenty three!
(iii) I am a special number
Take away from me a six!
A whole cricket team
You will still be able to fix!
(iv) Tell me who I am
I shall give a pretty clue!
You will get me back
If you take me out of twenty two!
30. Solve the following riddles, you may yourself construct such riddles.
Who am I?
(i) Go round a square
Counting every corner
Thrice and no more!
Add the count to me
To get exactly thirty four!
(ii) For each day of the week
Make an upcount from me
If you make no mistake
You will get twenty three!
(iii) I am a special number
Take away from me a six!
A whole cricket team
You will still be able to fix!
(iv) Tell me who I am
I shall give a pretty clue!
You will get me back
If you take me out of twenty two!
Explanation:
(i) Square has 4 corners.
Three times the number is = 3 × 4 = 12
When number is added with 12 it becomes 34
So, the number is = 34 – 12 = 22
(ii) The number given is 23, Up-counting for a week means 23–7=16
(iii) Let the number is x. So,
⇨ x – 6=11
⇨ x = 11 + 6 = 17
(iv) Let the number is x. So, 22 – x = x
⇨ 2x = 22, x = 11
Also Read: Chapter 12: Ratio and Proportion
