## 2310.21 – Coffee Break

Your boss took everyone for a coffee break. A look at the check told you that she paid $15.75 for three sandwiches, seven cups of coffee, and one piece of pie. Next time, the check was exactly $21 for four sandwiches, ten cups of coffee, and one piece of pie.

If you go by yourself tomorrow and have a sandwich, a cup of coffee, and a piece of pie, what will you pay?

## Solution

We are told that

$\begin{aligned}
3s + 7c + 1p &= 15.75 \\
4s + 10c + 1p &= 21.00,
\end{aligned}$

where $s$, $c$, and $p$ are the prices of individual sandwiches, cups of coffee and pieces of pie. Let's multiply the first equation by 3 and the second equation by 2:

$\begin{aligned}
9s + 21c + 3p = 47.25 \\
8s + 20c + 2p = 42.00.
\end{aligned}$

Subtracting the second from the first:

$s +c + p = 5.75.$

Voila!