SOLUTION: Kate's father is 3 years more than twice as old as Kate. The product of their ages in years is 560. How old is Kate?

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Question 983410: Kate's father is 3 years more than twice as old as Kate. The product of their ages in years is 560. How old is Kate?
Found 2 solutions by josgarithmetic, Timnewman:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
y, father
k, kate
system%28y=3%2B2k%2Cyk=560%29

%282k%2B3%29%2Ak=560
2k%5E2%2B3k-560=0
Factoring should be possible but general solution formula might be more comfortable than checking for the combinations.

k=%28-3%2Bsqrt%289%2B4%2A2%2A560%29%29%2F4
highlight%28k=25%2F2=highlight%2812%261%2F2%29%29

Answer by Timnewman(323) About Me  (Show Source):
You can put this solution on YOUR website!
Let Kate's age be "x"
Twice kate's age =2x
Kate's Father's age =3+2x
But the product of kate's ge and her father's age is 560,
then,
x(3+2x)=560
multiply out
3x+2x²=560
3x+2x²-560=0
2x²+3x-560=0
factorize the quadratic equation and get;
(2x+35)(x-16)=0
then,
2x+35=0 or x-16=0
x=-35/2 or x=16
ingnore tha nagative sign
hence,x=16yrs
Kate's age is 16yrs
HOPE THIS HELPS;....
-----BEST REGARDS,
TIMNEWMAN---------