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 :

#"17x + 5y = 174 "#------1
&
#"x + y = 18 " #-----2

Solve these equations simultaneously, from second equation we get x = 18 - y

Put this in equation 1

#17*(18-y) + 5y = 174#

#306 - 17y +5y = 174#

#-12y = -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.