Question

A woman bought some large frames for ​$16 each and some small frames for ​$5 each at a closeout sale. If she bought 18 frames for ​$​167, find how many of each type she bought.

Answer 1

The woman bought 7 large frames and 11 small frames. This was determined by setting up a system of linear equations using the given prices and total cost, and then solving for the quantities of each type of frame.

Step-by-step explanation:

The question involves solving a system of linear equations to find out how many large and small frames a woman bought at a closeout sale. We are given that large frames cost $16 each and small frames cost $5 each. The woman bought a total of 18 frames for $167.

To solve the problem, let us define the following variables:

• L = number of large frames
• S = number of small frames

We can then set up the following two equations based on the information provided:

1. L + S = 18 (since the total number of frames is 18)
2. 16L + 5S = 167 (since the total cost of the frames is $167)

Solving this system of equations will allow us to find the values of L and S. Here are the steps:

1. First, we can multiply the first equation by 5, which gives us 5L + 5S = 90.
2. Then, subtract this equation from the second equation: (16L + 5S) - (5L + 5S) = 167 - 90, which simplifies to 11L = 77.
3. Dividing both sides by 11 gives us L = 7.
4. Plug L = 7 back into the first equation: 7 + S = 18, which simplifies to S = 11.

Therefore, the woman bought 7 large frames and 11 small frames.