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?

Question

30612 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-10-29T15:21:54

see below

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 :

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

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

Put this in equation 1

$17 \cdot (18 - y) + 5 y = 174$ $17*(18-y) + 5y = 174$

$306 - 17 y + 5 y = 174$ $306 - 17y +5y = 174$

$- 12 y = - 132$ $-12y = -132$

$y = 11$ $y = 11$

Put y = 11 in eq x = 18 - y

$x = 18 - y$ $x = 18 - y$

$x = 18 - 11$ $x = 18 - 11$

$x = 7$ $x= 7$

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