# A woman bought some large frames for $17 each and some small frames for$5 each at a close out sale. If she bought 18 frames for $174, how do you find how many of each type she bought? ##### 1 Answer Oct 29, 2016 see below #### Explanation: 1 Large frame costs = 17$

Therefore, x large frames costs = 17x ${where x is the number of large frames she bought} 1 Small frame costs = 5$

Therefore, x Small frames costs = 5y ${where y is the number of small frames she bought} By the given condition : $\text{17x + 5y = 174 }$------1 & $\text{x + y = 18 }$-----2 Solve these equations simultaneously, from second equation we get x = 18 - y Put this in equation 1 $17 \cdot \left(18 - y\right) + 5 y = 174$$306 - 17 y + 5 y = 174$$- 12 y = - 132$$y = 11$Put y = 11 in eq x = 18 - y $x = 18 - y$$x = 18 - 11$$x = 7\$

So the woman bought 7 large frames and 11 small frames.