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?
Let's assume the woman bought x large frames and y small frames.
According to the given information, the price of each large frame is $16, and the price of each small frame is $7.
Therefore, the total cost of x large frames would be 16x, and the total cost of y small frames would be 7y.
The total number of frames bought is 20. So, we have the equation:
x + y = 20 ---------------(1)
The total cost of the frames is $176. So, we also have the equation:
16x + 7y = 176 --------------(2)
To solve these two equations, we can use either substitution or elimination method.
Let's use the elimination method to solve the equations:
Multiply equation (1) by 7, and multiply equation (2) by -1 to eliminate y:
7x + 7y = 140
-16x - 7y = -176
Adding these two equations:
7x - 16x + 7y - 7y = 140 - 176
-9x = -36
Dividing both sides by -9:
x = 4
Now we can substitute this value of x into equation (1) to find y:
4 + y = 20
y = 20 - 4
y = 16
Therefore, she bought 4 large frames and 16 small frames.
To solve this problem, we can set up a system of equations based on the given information.
Let's assume the woman bought 'x' large frames and 'y' small frames.
According to the problem, she bought 20 frames in total, so we have the equation:
x + y = 20 (Equation 1)
The price of each large frame is $16, and the woman bought 'x' of them. So, the cost of the large frames is 16x.
Similarly, the price of each small frame is $7, and the woman bought 'y' of them. So, the cost of the small frames is 7y.
The total cost of all the frames is $176, so we have the equation:
16x + 7y = 176 (Equation 2)
Now, we have formed a system of equations with Equation 1 and Equation 2. We can solve this system of equations to find the values of 'x' and 'y'.
One way to solve this system is by substitution or elimination. Let's solve it using the substitution method.
From Equation 1, we have:
x = 20 - y
Substituting this value of 'x' into Equation 2, we get:
16(20 - y) + 7y = 176
Simplifying the equation, we have:
320 - 16y + 7y = 176
320 - 9y = 176
-9y = 176 - 320
-9y = -144
Dividing both sides by -9, we get:
y = (-144) / (-9)
y = 16
Substituting the value of y back into Equation 1, we have:
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.
large frames ---- x
small frames ---- 20-x
16x + 7(20 - x) = 176
solve, should be very straightforward