a pottery studio gives three-hour and five-hour classes for $41.00 an hour. The studio collects 6,437 for 41 classes. How many 3 hour classes and how many five hour classes were paid for?

Answer 1

number of 3-hour classes --- x
number of 5-hour classes --- y

x+y = 41 ----> y = 41-x

3(41)x + 5(41)y = 6437
3x + 5y = 157
sub in the 1st equation ...

3x + 5(41-x) = 157
3x + 205 - 5x = 157
-2x = -48
x = 24
then y = 41-24 = 17

they sold 24 three-hour courses and
17 five-hour courses

Answer 2

X 3-hour classes.
(41-x) 5-hour classes.

41(3x) + 41*5(41-x) = $6,437.
123x + 8405-205x = 6,437
-82x = 6437-8405 = -1968
X = 24 3-hour classes.

41-x = 41-24 = 17 5-hour classes.