SOLUTION: A man's age is three times the sum of the age of his two sons, one of whom is twice as old as the other; in 12 years the sum of the son's ages will be three-fourths of their fathe

Algebra ->  Customizable Word Problem Solvers  -> Age -> SOLUTION: A man's age is three times the sum of the age of his two sons, one of whom is twice as old as the other; in 12 years the sum of the son's ages will be three-fourths of their fathe      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1041077: A man's age is three times the sum of the age of his two sons, one of whom is twice as old as the other; in 12 years the sum of the son's ages will be three-fourths of their father's age. Find their respective ages.
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Father's Age              y
A Son's Age               b
The Other Son's Age       s

Follow the written description closely and translate into equations.

system%28y=3%28b%2Bs%29%2Cs=2b%2C%28b%2B12%29%2B%28s%2B12%29=%283%2F4%29%28y%2B12%29%29

Solve the system. FORMING the system of equations is the biggest part of the solution to the given problem description.

y=3%28b%2B2b%29
y=9b
-
b%2Bs%2B24=%283%2F4%29%28y%2B12%29
4b%2B4s%2B72=3y%2B36
4b%2B4s%2B36=3y
-
4b%2B4%2A2b%2B36=3y
12b%2B36=3y
4b%2B12=y
-
Simpler System, system%284b%2B12=y%2Cy=9b%29
-
Simple substitution for y, OR simply equating expressions for y,
4b%2B12=9b
12=5b
b=12%2F5=2%262%2F5-----------this suggests that I made a mistake, because we usually expect Natural numbers for this kinds of age description exercises. You can keep working with it, or recheck my steps.