1. Problem: The cost of 3 hamburgers, 5 milk shakes, and 1 order of fries at a certain fast food restaurant is $\$ 23.50$. At the same restaurant, the cost of 5 hamburgers, 9 milk shakes, and 1 order of fries is $\$ 39.50$. What is the cost of 2 hamburgers, 2 milk shakes ,and 2 orders of fries at this restaurant?
Solution: Let $H=$ hamburger, $M=$ milk shake, and $F=$ order of fries. Then $3 H+5 M+F=\$ 23.50$. Multiplying the equation by 2 yields $6 H+10 M+2 F=\$ 47$. Also, it is given that $5 H+9 M+F=\$ 39.50$. Then subtracting the following equations
$$
\begin{array}{lll}
6 H+10 M+2 F & =\$ 47.00 \\
5 H+9 M+F & =\$ 39.50
\end{array}
$$
yields $H+M+F=\$ 7.50$. Multiplying the equation by 2 yields $2 H+2 M+2 F=\$ 15$.