systems of equations

Question

A pottery studio gives 3 hour and 5 hour classes for $29 an hour. If the studio has collected $4466 for a total of 42 classes, how many three hour classes and how many five hour classes were paid for?

Answer 1

Let x = the number of 3 hour classes.  Since there were 42 classes in total, the number of 5 hour classes is 42-x.  The cost of a 3 hour class is (3 hours)*($29) = $87.  The cost of the 5 hour class is 5*$29 = $145.

 

$4466 = x*($87) + (42-x)*($145)

 

$4466 = 87x + 6090 - 145x

 

-$1624 = -58x

 

Solve for x, the number of 3 hour classes.  Once you have x, the number of 5 hour classes is 42-x.