linear equation word problems

Question

I need to write linear equations for the hotdog and the cheesburgers or I need to solve them.

At the baseball game the Kacanich family purchased 3 hot dogs and 2 cheeseburgers and paid $31.25. The Nisbet family purchased 5 hot dogs and 2 cheeseburgers and paid $41.75. Write and solve a linear system to find the cost of each hot dog and each cheeseburger.

Answer 1

Let $x$ be the number of hotdogs purchased.

Let $y$ be the number of cheeseburgers purchased.

If 3 hot dogs and 2 cheeseburgers cost $31.25. then $3x + 2y = 31.25$.

If 5 hot dogs and 2 cheeseburgers cost $41.75. then $5x + 2y = 41.27$.

Now solve for $x$ and $y$. To solve for $x$ you can subtract both equations to get $2x = 41.27-31.25=10.02$ so $x = \frac{10.02}{2} = 5.01$.

Now to solve for $y$ you could replace $x$ in any equation say the first one to get $2y = 31.25 - 3(5.01)=16.22$ so $y = 8.11$.