Question

pottery studio gives three-hour and four-hour ceramics classes for $36 an hour. If the studio has collected $4428 for a total of 32 classes, how many three hour classes and how many four-hour classes were paid for?

Answer 1

5 three hour classes and 27 four hour classes

Explanation:

Convert these words into equations

Since one hour is 36, we can write two expressions for the 2 different classes: 108x and 144y (the amount of money from those classes)

x is the number of 3 hour classes, y is the number of 4 hour classes

Since the amount of money the studio makes is 4428, 108x+144y=4428

Since there are a total of 32 classes, x+y=32

So we now have the equations x+y=32 and 108x+144y=4428

Solve for x in the first equation (in order to substitute it into the second one)

we get x=32-y

plugging this into the second equation gives

108(32-y)+144y=4428

3456-108y+144y=4428

Combining like terms gives 36y=972

y=27

So there are 27 four hour classes, and 5 three hour classes( because 32-27=5)