(Can someone please help?)
A woman bought some large frames for $16 each and some small frames for $7 each at a closeout sale. If she bought 20 frames for $176, find how many of each type she bought?
She bought ___ large frames?
She bought ___ small frames?
To solve this problem, let's assume that the woman bought 'x' large frames and 'y' small frames.
Given:
Large frames cost $16 each
Small frames cost $7 each
The total number of frames bought is 20
The total amount spent on frames is $176
So, we can set up two equations based on the given information.
Equation 1: x + y = 20 (since the total number of frames bought is 20)
Equation 2: 16x + 7y = 176 (since the total amount spent on frames is $176)
To solve this system of equations, we can use either the substitution method or the elimination method. Let's use the substitution method here.
From Equation 1, we can express one variable in terms of the other. Let's solve for x:
x = 20 - y
Substitute this value of x into Equation 2:
16(20 - y) + 7y = 176
Now, we can simplify and solve for y:
320 - 16y + 7y = 176
320 - 9y = 176
-9y = 176 - 320
-9y = -144
y = -144 / -9
y = 16
Now, substitute the value of y back into Equation 1 to solve for x:
x + 16 = 20
x = 20 - 16
x = 4
Therefore, the woman bought 4 large frames and 16 small frames.
She bought 4 large frames.
She bought 16 small frames.
done here
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