How many frames each?

Question

A woman bought some large frames for

​$12

each and some small frames for

​$5

each at a closeout sale. If she bought

15

frames for

​$110

find how many of each type she bought.

Answer 1

Because you have two unknowns, you must have two equations.

Let's use the letters L for the # of large frames & S for the # of small frames.

We know that the TOTAL # of frames is 15, so your first equation is easy: L + S = 15.

To find a total cost for each type of frame, remember you'd multiply the quantity by the cost. So to find the total cost for the large frames you'd use 12L, and similarly for the small frames you'd use 5S. Then to find the TOTAL Dollar amount you'd add these two values together, making: 12L + 5S = 110.

Now you have your two equations. Use matrices, substitution (easiest here), or elimination (also pretty simple) to find L & S.

Answer 2

This is a system of equations problem.

Let's say the woman bought X large frames at $12 each and Y small frames at $5 for $110:

12x + 5y = 110

Next, we know that she bought 15 frames altogether:

x + y = 15

Using elimination you can find the value of x. Multiply the equation x + y = 15 by -5 as follows:

12x + 5y = 110

-5(x) + -5(y) = -5(15)

12x + 5y = 110

-5x + -5y= -75

7x = 35

x=5

Now, we can substitute 5 for x:

5 + y = 15

y = 15-5

y=10

Therefore, the woman bought 5 large frames and 10 small frames.