Question 1054852
a woman is 4 times older than her daughter. 
<pre>
W = 4D
</pre>
5 years ago, 
<pre>
That was when the woman was W-5
That was when the daughter was D-5
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the product of their ages was 175. 
<pre>
(W-5)(D-5) = 175

{{{system(W=4D,(W-5)(D-5)=175)}}}

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</pre></b>