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Pottery studio

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2 Answers

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
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