SOLUTION: a woman is 4 times older than her daughter. 5 years ago, the product of their ages was 175. find their present ages

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Question 1054852: a woman is 4 times older than her daughter. 5 years ago, the product of their ages was 175. find their present ages
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
a woman is 4 times older than her daughter. 
W = 4D

5 years ago, 
That was when the woman was W-5
That was when the daughter was D-5

the product of their ages was 175. 
(W-5)(D-5) = 175

system%28W=4D%2C%28W-5%29%28D-5%29=175%29

Substitute 4D for W in the second equation:

(4D-5)(D-5) = 175

4Dē-20D-5D+25 = 175

4Dē-25D+25 = 175

4Dē-25D-150 = 0

(4D+15)(D-10) = 0

4D+15=0;      D-10=0
   4D=-15;       D = 10
    D=-15/4;

Ignore the negative fraction answer.

The Daughter is 10.

The woman is 4D = 4(10) = 40.

Checking: 5 years ago the woman was 35 and her daughter was 5.
And sure enough 5 times 35 is 175.

Edwin