SOLUTION: A woman is 4 time older than her child.5 years ago the product of their ages was 175.find their present ages

Question 1091203: A woman is 4 time older than her child.5 years ago the product of their ages was 175.find their present ages
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
w = the woman's present age
c = the child's
:
Write an equation for each statement
:
A woman is 4 time older than her child.
w = 4c
5 years ago the product of their ages was 175.
(w-5)*(c-5) = 175
replace w with 4c
(4c-5)*(c-5) = 175
FOIL
4c^2 - 20c - 5c + 25 = 175
4c^2 - 25c + 25 - 175 = 0
a quadratic equation
4c^2 - 25c - 150 = 0
We can use the quadratic formula; a=4; b=-25; c=-150, but this will factor to
(4c+15)(c-10) = 0
the positive solution is all we want here
c = 10 yrs old the child's age
then obviously
4(10) = 40 yrs is the woman's age
:
:
Check this solution in the statement
"5 years ago the product of their ages was 175"
(40-5) * (10-5) =
35 * 5 = 175
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