A girl is currently 5yrs older than her younger brother and three yrs younger then her older brother. Two yrs from the current time, the product of the brothers ages will be tweleve times the age of the girl. What is the current age of the older brother?

Question

mertsj · Answer

x=girl's age
x-5 = age of younger brother
x+3= age of older brother
IN TWO YEARS:
x+2 = girl's age
x-5+2=x-3 = age of younger brother
x+3+2=x+5 = age of older brother
(x-3)(x+5)=12(x+2)

mertsj · Answer

x^2+2x-15=12x+24
x^2-10x-39=0
(x-13)(x+3)=0
x=13 or -3
Reject -3 as the girl's age is not negative
So the girl is 13, her younger brother is 8 and her older brother is 16