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*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.

User Bmiller
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1 Answer

1 vote

Answer:

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.

User Ingo Leonhardt
by
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