Question

PLZZ HELP ASAP two numbers are in the ratio 5 : 8. If 9 is added to each number, we get a new ratio 8 : 11. Find the numbers.

Answer 1

15 and 24

Explanation:

the ratio of the 2 numbers = 5 : 8 = 5x : 8x ( x is a multiplier ), then

5x + 9 : 8x + 9 = 8 : 11

Expressing the rations in fractional form

`(5x + 9)/(8x + 9)` =
`(8)/(11)` ( cross- multiply )

8(8x + 9) = 11(5x + 9) ← distribute parenthesis on both sides

64x + 72 = 55x + 99 ( subtract 55x from both sides )

9x + 72 = 99 ( subtract 72 from both sides )

9x = 27 ( divide both sides by 9 )

x = 3

Thus the 2 numbers are

5x = 5 × 3 = 15

8x = 8 × 3 = 24

Answer 2

let the number be 8x and 9x

5x+9 = 8

8x+9 11

55x+99=64x + 72

64x-55x= 99-72

9x=27

x=3

so the required numbers are

5x+9=5*3+9=24

8x+9= 33