SOLUTION: the square of my youngest child's age is 9 more then the product of 17 and the age of my oldest child. my oldest child is 3 years older than my youngest child. How old are my child

Algebra ->  Customizable Word Problem Solvers  -> Age -> SOLUTION: the square of my youngest child's age is 9 more then the product of 17 and the age of my oldest child. my oldest child is 3 years older than my youngest child. How old are my child      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 772235: the square of my youngest child's age is 9 more then the product of 17 and the age of my oldest child. my oldest child is 3 years older than my youngest child. How old are my children?

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
x= age of youngest child
y= age of oldest child
So
x%5E2= the square of the youngest child's age
17y= the product of 17 and the age of the oldest child
17y%2B9= 9 more then the product of 17 and the age of the oldest child
"The square of my youngest child's age is 9 more then the product of 17 and the age of my oldest child" translates as
x%5E2=17y%2B9
"My oldest child is 3 years older than my youngest child" translates as
y=x%2B3

We need to solve the system
system%28x%5E2=17y%2B9%2Cy=x%2B3%29
Substituting y=x%2B3 into the other equation we get
x%5E2=17%28x%2B3%29%2B9 --> x%5E2=17x%2B51%2B9 --> x%5E2=17x%2B60 --> x%5E2-17x-60=0
That quadratic equation can be solved several ways.
For me, the easiest way is by factoring:
x%5E2-17x-60=0 --> %28x-20%29%28x%2B3%29=0
The solutions are:
x-20=0 --> highlight%28x=20%29 and
x%2B3=0 --> x=-3, which does not make sense, because no person can have a negative age.
From highlight%28x=20%29 (and y=x%2B3), we get
y=20%2B3--> highlight%28y=23%29