Question 772235
{{{x}}}= age of youngest child
{{{y}}}= age of oldest child
So
{{{x^2}}}= the square of the youngest child's age
{{{17y}}}= the product of 17 and the age of the oldest child
{{{17y+9}}}= 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^2=17y+9}}}
"My oldest child is 3 years older than my youngest child" translates as
{{{y=x+3}}}
 
We need to solve the system
{{{system(x^2=17y+9,y=x+3)}}}
Substituting {{{y=x+3}}} into the other equation we get
{{{x^2=17(x+3)+9}}} --> {{{x^2=17x+51+9}}} --> {{{x^2=17x+60}}} --> {{{x^2-17x-60=0}}}
That quadratic equation can be solved several ways.
For me, the easiest way is by factoring:
{{{x^2-17x-60=0}}} --> {{{(x-20)(x+3)=0}}}
The solutions are:
{{{x-20=0}}} --> {{{highlight(x=20)}}} and
{{{x+3=0}}} --> {{{x=-3}}}, which does not make sense, because no person can have a negative age.
From {{{highlight(x=20)}}} (and {{{y=x+3}}}), we get
{{{y=20+3}}}--> {{{highlight(y=23)}}}