Question 1194795: A woman is 3 times as old as her son. 8 years ago the product of their ages was 112. Find their present ages. Found 2 solutions by ikleyn, MathLover1:Answer by ikleyn(52788) (Show Source):
You can put this solution on YOUR website! .
A woman is 3 times as old as her son. 8 years ago the product of their ages was 112.
Find their present ages.
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Let their present age be x for the son and 3x for the mother.
8 years ago they were (x-8) and (3x-8) years old, respectively.
An equation from the other part of the problem is
(x-8)*(3x-8) = 112.
Simplify
3x^2 - 8x - 24x + 64 = 112
3x^2 - 32x -48 = 0
Solve using the quadratic formula.
You will get two roots of the equation: one positive integer of 12, and the other
negative rational -1.
Use positive integer root and ignore negative one.
ANSWER. The son is 12 years old; the mother is 36 years old.
CHECK. (12-8)*(36-8) = 4*28 = 112. ! Correct !
You can put this solution on YOUR website!
let woman’s age be and son’s age
if a woman is times as old as her son, we have
..........eq.1
if years ago the product of their ages was ........eq.2
from eq.1 and eq.2 we have
we need integer solution, so
then ..........eq.1
their present ages: woman is and son is years old
check the product of their ages years ago
years ago woman was and son was which confirms our result
