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?

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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

Michael A. | Math/Physics/Science TutorMath/Physics/Science Tutor

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

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