SOLUTION: The sum of the ages of Alan, Jim, and Les is 157 years. Twenty years ago, six times Jim's age was equal to seven times Alan's age. In eight years, Les will be three times as old a

Algebra ->  College  -> Linear Algebra -> SOLUTION: The sum of the ages of Alan, Jim, and Les is 157 years. Twenty years ago, six times Jim's age was equal to seven times Alan's age. In eight years, Les will be three times as old a      Log On


   



Question 994115: The sum of the ages of Alan, Jim, and Les is 157 years. Twenty years ago, six times Jim's age was
equal to seven times Alan's age. In eight years, Les will be three times as old as Alan was 30 years
ago. Find their ages now.
Please help to solve the problem above. Algebra 2. Thank you.

Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
The exercise could also be for Algebra 1.

a, Allen's age
j, Jim's age
L, Les's age

Each part of the description can be literally transcribed.
system%28a%2Bj%2BL=157%2C6%28j-20%29=7%2A%28a-20%29%2C%28L%2B8%29=3%28a-30%29%29

Use your concepts and skills to simplify the system of equations.
-
a%2Bj%2BL=157, good as it is.
-
6j-120=7a-140
7a-140=6j-120
7a-6j-140=-120
7a-6j=20
-
L%2B8=3a-90
3a-90=L%2B8
3a-L=8%2B90
3a-L=98


The equivalent linear system is
highlight%28system%28a%2Bj%2BL=157%2C7a-6j%2B0%2AL=20%2C3a%2B0%2Aj-L=98%29%29

Are you good with a system like this or do you still need help?