Question

Rose is two thirds as old as Johnny, in 5yrs the sum of their ages will be 50yrs, how do you find their present ages?

Answer 1

Rose is 16
Johnny is 24

Explanation:

Define
`color(white)("XXX")r`: Rose's age
`color(white)("XXX")j`: Johnny's age

We are told
`color(white)("XXX")r=2/3j`

`color(white)("XXX")rarrcolor(white)("XXX")"[1]"color(white)("XXX")3r-2j=0`

and
`color(white)("XXX")(r+5)+(j+5) = 50`

`color(white)("XXX")rarrcolor(white)("XXX")"[2]"color(white)("XXX")r+j = 40`

Multiplying [2] by 2
`color(white)("XXXXXXXX")[3]color(white)("XXX")2r + 2j = 80`

Adding [1] and [3]
`color(white)("XXXXXXXX")[4]color(white)("XXX")5r = 80`

Dividing [4] by `5`
`color(white)("XXXXXXXX")[5]color(white)("XXX")r=16`

Substituting `16` for `r` in [1] (and simplifying
`color(white)("XXXXXXXX")[6]color(white)("XXX")j=24`