Two numbers are in the ratio 3:2. if 5 subtracted to each the new ratio becomes 2:3 find the numbers.
> Solution

3 and 2

Step-by-step explanation:

The ratio of the 2 numbers = 3 : 2 = 3x : 2x ( x is a multiple )

When 5 is subtracted from both , that is

3x - 5 : 2x - 5 = 2 : 3

Expressing the ratio in fractional form

= ( cross- multiply )

3(3x - 5) = 2(2x - 5) ← distribute both sides

9x - 15 = 4x - 10 ( subtract 4x from both sides )

5x - 15 = - 10 ( add 15 to both sides )

5x = 5 ( divide both sides by 5 )

x = 1

Thus the 2 numbers are

3x = 3(1) = 3 and 2x = 2(1) = 2