Question

*4.3.11 A woman bought some large frames for ​$11 each and some small frames for ​$8 each at a closeout sale. If she bought 26 frames for ​$232​, find how many of each type she bought.

Answer 1

She bought 8 large frames and 18 small frames of each type.

Explanation:

Given:

A woman bought some large frames for ​$11 each and some small frames for ​$8 each at a closeout sale.

If she bought 26 frames for ​$232​.

Now, to find each type she bought.

Let the number of large frames for $11 be
`x.`

And let the number of small frames for $8 be
`y.`

So, the total number of frames:

`x+y=26`

`x=26-y\ \ \ \ .........(1)`

Now, the total cost of frames:

`11x+8y=232`

Substituting the value of
`x` from equation (1) we get:

`11(26-y)+8y=232`

`286-11y+8y=232`

`286-3y=232`

Subtracting both by sides 286 we get:

`-3y=-54`

Dividing both sides by -3 we get:

`y=18.`

The number of small frames = 18.

Now, substituting the value of
`y` in equation (1) to get the value of
`x`:

`x=26-y\\\\x=26-18\\\\x=8.`

The number of large frames = 8.

Therefore, she bought 8 large frames and 18 small frames of each type.