Question 352215
First name your variables.
How about {{{A}}} and {{{B}}}?
Now turn the words into equations.
"sum of two numbers is 31"
1.{{{A+B=31}}}
"product of the two numbers is 150"
2.{{{A*B=150}}}
From eq. 1,
{{{A+B=31}}}
{{{A=31-B}}}
Substitute into eq. 2,
{{{A*B=150}}}
{{{(31-B)*B=150}}}
{{{31B-B^2=150}}}
{{{B^2-31B+150=0}}}
You can factor this equation,
{{{(B-25)(B-6)=0}}}
Two solutions:
{{{B-25=0}}}
{{{highlight(B=25)}}}
Then from eq. 1,
{{{A+25=31}}}
{{{highlight(A=6)}}}
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{{{B-6=0}}}
{{{highlight_green(B=6)}}}
Then from eq. 1,
{{{A+6=31}}}
{{{highlight_green(A=25)}}}
Your two numbers are 6 and 25.
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You're studying quadratic equations in the 4th grade??