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
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