Question

Two numbers are in the ratio 3: 7. If 1 is added to the smaller number and 7 is added to the larger, they will be in the ratio 1: 3. Find the numbers.

Answer 1

6 and 14

Explanation:

The numbers are in the ratio 3 : 7 = 3x : 7x (x is a multiplier )

adding 1 to smaller number is 3x + 1 and 7 to the larger is 7x + 7, then

3x + 1 : 7x + 7 = 1 : 3

Expressing the ratio in fractional form

`(3x+1)/(7x+7)` =
`(1)/(3)` ( cross- multiply )

3(3x + 1) = 7x + 7

9x + 3 = 7x + 7 ( subtract 7x from both sides )

2x + 3 = 7 ( subtract 3 from both sides )

2x = 4 ( divide both sides by 2 )

x = 2

Thus the numbers are

3x = 3(2) = 6

7x = 7(2) = 14