SOLUTION: at present five times the square ofa daughters age is 8 years less than the mothers age.after two years seventimes the daughters age would be 2years less than that time .find the p

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Question 1020203: at present five times the square ofa daughters age is 8 years less than the mothers age.after two years seventimes the daughters age would be 2years less than that time .find the present age of the daughter.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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let d = daughter's present age
let m = the mother's
:
Write an equation for each statement
:
at present five times the square of a daughters age is 8 years less than the mothers age.
5d^2 = m - 8
m = 5d^2 + 8
:
after two years seven times the daughters age would be 2years less than the mother at that time .
7(d + 2) = (m + 2) - 2
7d + 14 = m
replace m with (5d^2+8)
7d + 14 = 5d^2 + 8
Arrange as a quadratic equation
0 = 5d^2 - 7d + 8 - 14
5d^2 - 7d - 6 = 0
use the quadratic formula to find d, a=5; b=-7; c=-6, but this will factor
(d - 2)(5d + 3) = 0
The positive solution is all we want here
d = 2 yrs is the daughter's present age
:
:
:
See if that checks out in the 1st statement, find m
m = 7(2) + 14
m = 28 yrs is mom's age
"at present five times the square of a daughters age is 8 years less than the mothers age."
5(2^2) = 28 - 8
5(4) = 20