The sum of two numbers is $19$ and their difference is $5$. What is their product?
I need to find two numbers that add up to $19$ and subtract to $5$. I can also try to use algebra and solve a system of equations. Let me call the two numbers $x$ and $y$. Then I have $x + y = 19$ and $x - y = 5$. I can add these two equations and get $2x = 24$, so $x = 12$. Then I can plug $x = 12$ into either equation and get $y = 7$. So the two numbers are $12$ and $7$. To find their product, I just multiply them together: $12 \times 7 = 84$. 