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

3s+7c+1p=15.754s+10c+1p=21.00,\begin{aligned}3s + 7c + 1p &= 15.75 \\4s + 10c + 1p &= 21.00,\end{aligned}

where ss, cc, and pp 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:

9s+21c+3p=47.258s+20c+2p=42.00.\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.s +c + p = 5.75.

Voila!