Question

A woman bought some large frames for $15 each and some small frames for $7 each at a closeout sale. If she bought 23 frames for $193, find how many of each type she bought.

Answer 1

`\begin{gathered} x=\text{ number of large frames} \\ y=Number\text{ of small frames} \\ 15\text{ cost of large frames} \\ 7\text{ cost of small frames} \\ 23\text{ frames} \\ 193\text{ total cost} \\ Equation\text{ system} \\ x+y=23\text{ (1)} \\ 15x+7y=193\text{ (2)} \\ \text{From (1) solving x} \\ x=23-y \\ U\sin g\text{ x in (2)} \\ 15x+7y=193 \\ 15(23-y)+7y=193 \\ 345-15y+7y=193 \\ -15y+7y=193-345 \\ -8y=-152 \\ y=(-152)/(-8) \\ y=19 \\ With\text{ the value of y} \\ x=23-19 \\ x=4 \\ \text{The bought 4 large frames and 19 small frames} \end{gathered}`