SOLUTION: a father is 24 years older than the son if the ratio of their age is 5:2 find the age of the son

Algebra ->  Customizable Word Problem Solvers  -> Age -> SOLUTION: a father is 24 years older than the son if the ratio of their age is 5:2 find the age of the son      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1124900: a father is 24 years older than the son if the ratio of their age is 5:2 find the age of the son
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
let's father's age be x and son's age y
if father is 24 years older than the son, we have
x=y%2B24...eq.1

if the ratio of their age is 5%3A2, we have
x%3Ay=5%3A2....eq.2.....solve or x
2x=5y
x=5y%2F2....eq.2a
from eq.1 and eq.2a we have
5y%2F2=y%2B24...solve or y
5y=2y%2B48
5y-2y=48
3y=48
y=48%2F3
highlight%28y=16%29
find x:
x=y%2B24...eq.1
x=16%2B24
highlight%28x=40%29
so, father is highlight%2840%29 years old, and son is highlight%2816%29 years old

check the ratio:
x%3Ay=5%3A2
40%3A16=5%3A2...simplify left side
5%3A2=5%3A2 -> which confirms our solution