Question

Harvey is 3 times as old as Jane. The sum of their ages is 48 years. What is the age of each?

Answer 1

`"Jane's' age" = 12years and "Harvey's age" = 36years`

Explanation:

Let `"Jane's' age" = x`

Hence, Harvey is `3 xx` as old as Jane

`:. "Harvey's age" = 3 xx x = 3x`

Sum of their ages..

`"Jane's' age" (x) + "Harvey's age" (3x) = 48`

`x + 3x = 48`

`4x = 48`

Divide both sides by `color(red)4`

`(4x)/color(red)4 = 48/color(red)4`

`cancel(4x)/cancel4 = 48/4`

`x = 48/4`

`x = 12`

Substituting each values..

`"Jane's' age" = x`

`"Jane's' age" = 12years`

and..

`"Harvey's age" = 3x`

`"Harvey's age" = 3(12)`

`"Harvey's age" = 36years`