Question

Find two numbers if their sum 16 and their ratio is 5:7

Answer 1

6.666 or 6 2/3 and 9. 333 or 9 1/3

Explanation:

5+7 = 12 so 1 part is 1

16/12 = 1.333.. = 1 1/3 1 part is changed when the total is higher

5 x 1 1/3 = 6.666 6 2/3

7 x 1 1/3 = 9. 333 = 9 1/3

Answer 2

Explanation:

Let A and B stand for the two numbers.

A + B = 16

A/B = 5/7

Rearrange the first and substitute:

A = 16-B

(16-B)/B = 5/7

(16-B) = 5B/7

5B/7 = (16-B)

5B = 7(16-B)

5B = 112 - 7B

12B = 112

B = 9.3333 or 9 1/3

A = (16 - 9.333) or (16 - 9 1/3)

A = 6.6667 or 6 2/3

A + B = 16?

9 1/3 + 6 2/3 = 16 YES

A/B = 5/7 ?

(6 2/3)/(9 1/3) = (20/3)/(28/3) = (20/3)*(3/28)

= (20/28) = 5/7 YES