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Answer to Question #16970 in Algebra for bluerose

Question #16970
word problem involving quadratic equation
mich is 10 times older than her daughter anne. in five years,the product of her age and anne's age was 175years.how old are each at present?
Expert's answer
Mich is X years old, Anne is Y years old.Mich is 10 times older than her daughter Anne: X = 10 * Y.
In five years, the product of her age and Anne's age was 175 years:
(X + 5) * (Y + 5) = 175.
(10 * Y + 5) * (Y + 5) = 17510 * Y^2 + 5 * Y + 10 * Y * 5 + 5 * 5 = 175
10 * Y^2 + 55 * Y + 25 = 175
2 * Y^2 + 11 * Y + 5 = 352 * Y^2 + 11 * Y - 30 = 0
Y = { -11 ± Sq Root ( 121 + 240 ) } / 4 = {2, - 7.5}
At present, Anne is 2 years old and Mich is 10 * 2 = 20 years old.

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