Question

i am in trouble with math help

Answer 1

2
⇒ x = 6/8 = 3/4

2. The perimeter of a rectangular swimming pool is 154 m. Its length is 2 m more than twice its breadth. What are the length and the breadth of the pool?

Answer

Given,
Perimeter of rectangular swimming pool = 154 m
Let the breadth of rectangle be x.
A/q,
Length of the rectangle = 2x + 2
Perimeter = 2(length + breadth)
⇒ 2(2x + 2 + x) = 154 m
⇒ 2(3x + 2) = 154
⇒ 3x + 2 = 154/2
⇒ 3x = 77 - 2
⇒ x = 75/3
⇒ x = 25 m
Thus,
Breadth = x = 25 m
Length = 2x + 2 = 50 + 2 = 52 m

3. The base of an isosceles triangle is 4/3 cm. The perimeter of the triangle is 62/15 cm. What is the length of either of the remaining equal sides?

Answer

Base of isosceles triangle = 4/3 cm
Perimeter of triangle = 62/15 cm
Let the length of equal sides of triangle be x.
A/q,
4/3 + x + x = 62/15 cm
⇒ 2x = (62/15 - 4/3) cm
⇒ 2x = (62 - 20)/15 cm
⇒ 2x = 42/15 cm
⇒ x = 42/15 × 1/2
⇒ x = 42/30 cm
⇒ x =7/5 cm
The length of either of the remaining equal sides are 7/5 cm.

4. Sum of two numbers is 95. If one exceeds the other by 15, find the numbers.

Answer

Let the one of the number be x.
Then, other number will be x + 15
A/q,
x + x + 15 = 95
⇒ 2x + 15 = 95
⇒ 2x = 80
⇒ x = 40
First number = x = 40
Other number = x + 15 = 40 + 15 = 55

5. Two numbers are in the ratio 5:3. If they differ by 18, what are the numbers?

Answer

Let the two numbers be 5x and 3x.
A/q,
5x - 3x = 18
⇒ 2x = 18
⇒ x = 9
Thus, the numbers are 5x = 45 and 3x = 27.

6. Three consecutive integers add up to 51. What are these integers?

Answer

Let the three consecutive integers are x, x+1 and x+2.
A/q,
x + (x+1) + (x+2) = 51
⇒ 3x + 3 = 51
⇒ 3x = 51 - 3
⇒ 3x = 48
⇒ x = 16
Thus, the integers are x = 16, x+1 = 17 and x+2 = 18

7. The sum of three consecutive multiples of 8 is 888. Find the multiples.

Answer

Let the three consecutive multiples of 8 are 8x, 8(x+1) and 8(x+2).
A/q,
8x + 8(x+1) + 8(x+2) = 888
⇒ 8 (x + x+1 + x+2) = 888 (Taking 8 as common)
⇒ 8 (3x + 3) = 888
⇒ 3x + 3 = 888/8
⇒ 3x + 3 = 111
⇒ 3x = 108
⇒ x = 36
Thus, the three consecutive multiples of 8 are 8x = 8 × 36 = 288,
8(x+1) = 8 × (36+1) = 8 × 37 = 296 and
8(x+2) = 8 × (36+2) = 8 × 38 = 304

8. Three consecutive integers are such that when they are taken in increasing order and multiplied by 2, 3 and 4 respectively, they add up to 74. Find these numbers.

Answer

Let the three consecutive integers are x, x+1 and x+2.
A/q,
2x + 3(x+1) + 4(x+2) = 74
⇒ 2x + 3x +3 + 4x + 8 = 74
⇒ 9x + 11 = 74
⇒ 9x = 74 - 11
⇒ x = 63/9
⇒ x = 7
Thus, the numbers are x = 7, x+1 = 8 and x+2 = 9

9. The ages of Rahul and Haroon are in the ratio 5:7. Four years later the sum of their ages will be 56 years. What are their present ages?

Answer

Let the ages of Rahul and Haroon be 5x and 7x.
Four years later their age will be (5x + 4) and (7x + 4) respectively.
A/q,
(5x + 4) + (7x + 4) = 56
⇒ 5x + 4 + 7x + 4 = 56
⇒ 12x + 8 = 56
⇒ 12x = 56 - 8
⇒ x = 48/12
⇒ x = 4
Present age of Rahul = 5x = 5×4 = 20
Present age of Haroon = 7x = 7×4 = 28

10. The number of boys and girls in a class are in the ratio 7:5. The number of boys is 8 more than the number of girls. What is the total class strength?

Answer

Let the number of boys be 7x and girls be 5x.
A/q,
7x = 5x + 8
⇒ 7x - 5x = 8
⇒ 2x = 8
⇒ x = 4
Number of boys = 7×4 = 28
Number of girls = 5×4 = 20

11. Baichung’s father is 26 years younger than Baichung’s grandfather and 29 years older than Baichung. The sum of the ages of all the three is 135 years. What is the age of each one of them?

Answer

Let the age of Baichung’s father be x.
Therefor, Age of Baichung’s grandfather = (x+26)
and, Age of Baichung = (x-29)
A/q,
x + (x+26) + (x-29) = 135
⇒ 3x + 26 - 29 = 135
⇒ 3x = 135 + 3
⇒ 3x = 138
⇒ x = 138/3
⇒ x = 46
Age of Baichung’s father = x = 46
Ag1. If you subtract 1/2 from a number and multiply the result by 1/2, you get 1/8. What is the number?

Answer

Let the number be x.
A/q,
(x - 1/2) × 1/2 = 1/8
⇒ x/2 - 1/4 = 1/8
⇒ x/2 = 1/8 + 1/4
⇒ x/2 = 1/8 + 2/8
⇒ x/2 = (1+2)/8
⇒ x = 3/8 × 2
⇒ x = 6/8 = 3/4

2. The perimeter of a rectangular swimming pool is 154 m. Its length is 2 m more than twice its breadth. What are the length and the breadth of the pool?

Answer

Given,
Perimeter of rectangular swimming pool = 154 m
Let the breadth of rectangle be x.
A/q,
Length of the rectangle = 2x + 2
Perimeter = 2(length + breadth)
⇒ 2(2x + 2 + x) = 154 m
⇒ 2(3x + 2) = 154
⇒ 3x + 2 = 154/2
⇒ 3x = 77 - 2
⇒ x = 75/3
⇒ x = 25 m
Thus,
Breadth = x = 25 m
Length = 2x + 2 = 50 + 2 = 52 m

Answer 2

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