word problem help please?

Question

A woman bought some large frames for $14 each and some small frames for $4 each at a closeout sale. If she bought 26 frames for $204, find how many of each type she bought?

Answer 1

Let L represent the number of large frames she bought and S represent the number of small frames she bought. If she bought 26 total frames, then we know L+S=26. Since she spent 204 dollars then 14L+4S=204. Now we have two equations with two unknowns. To get a single equation with one variable, we will write L+S=26 in terms of L. Subtracting S from both sides we get L=26-S. Now, let's plug this in the second equation and solve for S.

 

14(26-S)+4S=204

364-14S+4S=204

364-10S=204

-10S=-160

S=16

 

If S=16 and L+S=26, then L=10.