Women bought some large frames for $18 each and some small frames for $6 each at a close out sale. If she bought 18 frames for $144, find how many of each type she bought?

Answer 1

Hi, Em,

Take what we know and try to get at least two equations from that information. We need as many equations as we have unknowns, which is two: the numbers of Large(L) and Small(S) frames.

We can relate the total amount spent ($144) to these two unknowns by stating that:

$144 = L*18 + S*6, where the numbers of each frame size are multiplied by their prices per frame of $18 and $6 for Large and Small.

We also know that a total of 18 frames were bought. That provides a second equation:

L + S = 18

I'll rewrite this as L = 18 - S and then substitute for L in the first equation:

144 = 18(18 - S) + 6S

144 = 324 - 18S + 6S

-180 = -12S

so then

S = 15 If S = 15, then L must be 3.

Check the quantities by using them in the first equation and see if the total bill adds to $144, which it does.

= 18*3 + 15*6 = 54 90 = $144

Always look for equations that tie together some elements of the problem in differing expressions. By rearranging and substituting, one can eventually arrive at a solution that involves just one of the unknowns. That solution can be used to find other unknowns, like we've done here.

I hope this helps,

Bob

Answer 2

18x + 6(18 - x) = 144; 12x = 144 - 108; 12x = 36, x = 3 and 18 - 3 = 15

Answer: woman bought 3 frames for $18 each and 15 frames by $6 each