Pottery studio

Question

A pottery studio gives two hour and five hour classes for $36 an hour. If the studio has collected $5976 for a total of 47 classes, how many two hour classes and how many five hour classes were paid for?

Answer 1

Let x = 2-hour classes

 

Let y = 5-hour classes

 

x + y = 47

 

72x + 180y = 5976

 

Multiply the top equation by 72

 

72x + 72y = 3384

 

72x + 180y = 5976

 

Subtract the first equation from the second

 

108y = 2592

 

y = 24

 

x = 23

 

There were 23 2-hour classes and 24 5-hour classes

Answer 2

Hey Larry, this is a classic two variable word problem.

 

let x = the number of 2 hour classes and y = the number of 5 hour classes.

 

Then we know that x + y = 47 right away.

 

To calculate the money portion, we consider where the money is coming from.  For every 2 hour class, it costs $36 an hour times 2, right.  So that is $72.  For the five hour class we have: 5 x 36 = $180.

 

The number of classes times the dollar amount will give us the total, so:

 

72x + 180y = 5976 and from above we have

   x  +      y = 47

 

This is our system of equations, which we can solve using SUBSTITUION or ELIMINATION.  For Substitution we can write:  y = 47-x and substitute this into the other equation:

 

72x + 180(47-x) = 5976

72x + 8460 - 180x = 5976

-108x + 8460 = 5976

-108x = -2484

x = 23

So y = 47-23 = 24

 

Can you solve this system using Elimination?

 

cheers