System Of Equations Type Problem

[dagr8est]

There are three people who are each under 30 years old. They have a total of 130 years of life left amongst them. The oldest has already lived half his life. The second oldest has already lived one third of his life. The youngest has also already lived one third of his life. If they all have whole number ages, find all possible sets of ages of the three people.

I'm not sure how to approach this problem. Here's what I have so far.

Let a, b, and c be the ages of the three people such that 0<c<b<a<30.

Then:
a = years left for oldest
2b = years left for second oldest
2c = years left for youngest
a+2b+2c = 130

That's where I'm stuck. Don't know what to do next. Any help will be appreciated.

 

[arthur ohlsten]

let a , b and c be the three present ages
then a has a years left to live
b has 2b years left
c has 2c years left
a+2b+2c=130 if each is now 30 then we have
30+60+60=150 so wecan reduce the ages
for a=28 we then have
b= 51 c=0
b=50 c= 1
b=49 c=2

you can finish it
Arthur

 

[dagr8est]

I see. Thanks.