Question

`8` years ago Carlos' age was four times that of his brother. In `18` years time he will be the double his brother's age. Now, what are the present ages of Carlos and his brother?

THANK YOU

Answer 1

Carlos is `60` and his brother is `21`

Explanation:

There are 3 periods of time:
past: ie `8` years ago
present
future: ie `18`years time

There are two people: Carlos and his brother.
Carlos is older

Let Carlos' present age be `x` and his brother be `y`

Write an expression for each person for each period of time:

`color(white)(wwwwww)" past future future"`
`Carlos: color(white)(www)(x-8)" "x" ("x+18)`
`Brother: color(white)(ww)(y-8)" "y" ("y+18)`

Now make equations:
In the past, Carlos was `4` times as old as his brother.

`4(y-8) = x-8" "rarr4y-32 = x-8" "rarrx -4y = -24`

In the future, Carlos will be twice as old as his brother.

`2(y+18)= x+18" "rarr 2y+36 =x+18" "rarrx-2y = 18`

We have 2 equations in `x and y`

`color(white)(wwwwwwww)x-4y = -24..................A`
`color(white)(wwwwwwww)x-2y =+18..................B`

`B-Acolor(white)(wwwwwww)2y = 42`
`color(white)(wwwwww.wwwww)y =21`

`2(y+18)= x+18`

`2(21+18)= x+18`

`2xx39 = x +18`

`x = 60`