#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 #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#