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?

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1 Answer
Jun 2, 2017

Carlos is 60 and his brother is 21

Explanation:

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