The athletic department manager purchased a total of 52 footballs and soccer balls. Each football cost $23.53, and each soccer ball cost $19.86. If the manager spent a total of $1,120.80, how many soccer balls did the manager purchase?

Since the information states that the athletic department manager purchased a total of 52 balls, you can say that the result of adding up the number of footballs and soccer balls purchased is 52, which can be expressed as:

x+y=52, where:

x is the number of footballs purchased

y is the number of soccer balls purchased

Also, as the statement indicates the price of each type of ball and the total cost, you can say that adding up the results of multiplying the price of each ball for the quantity purchased is equal to the total amount spent, which is:

23.53x+19.86y=1,120.80

Now, you have 2 equations:

x+y=52 (1)

23.53x+19.86y=1,120.80 (2)

To be able to find the value of x and y, first you can isolate x in (1):

x=52-y (3)

Then, you can replace (3) in (2) and solve for y:

23.53(52-y)+19.86y=1,120.80

1,223.56-23.53y+19.86y=1,120.80

1,223.56-1,120.80=23.53y-19.86y

102.76=3.67y

y=102.76/3.67

y=28

Finally, you can replace the value of y in (3) to find the value of x:

x=52-28

y=24

According to this, the answer is that the manager purchased 28 soccer balls.