A pottery studio gives three​-hour and four​-hour ceramics classes for ​$32 an hour. If the studio has collected ​$2592 for a total of 22 ​classes, how many thr

Question

how many three hour and how many four hour classes were paid for?

Answer 1

I would set this up and solve as a matrix.

 

Let x = # of 3-hour ceramics classes

Let y = # of 4-hour ceramics classes

 

No matter which class, there's a charge of $32/hour

We know that a total of 22 classes were done, in some combination of 3-hour and 4-hour ceramics classes

 

This gives us the following two equations:

 

1x   + 1y    =      22

96x + 128y = 2,592

 

This gives us the tableau for Iteration 0 of:

 

  1            1          =             22

96        128          =          2592

 

We want to get 1x = and 1y =, in order to solve for the x and y variables.  We begin this with a row operation to get the value in R2,C1 to equal 0:  -96R1 + R2 = new R2; which gives us the following Iteration 1 matrix:

 

1          1          =             22

0        32          =           480

 

Next, we want to get the value in R1,C2 to be a 0; so, we do the row operation of:  -R2 + 32R1 = new R1; which gives us the Iteration 2 matrix:

 

32          0          =          224  

  0        32          =          480

 

Then, we perform the following row reductions:

 

(1)   (1/32)R1 = new R1

(2)   (1/32)R2 = new R2

 

This gives us the following solution matrix of:

 

1          0          =            7

0          1          =          15

 

So, the solution set for (x,y) is:  (7,15)

 

We need to substitute these numbers into the original 2 equations, to perform a check of our numbers:

 

Check # 1:  7 + 15 = 22     [Check]

Check # 2:  96 * 7 + 128 * 15 = 2,592      [Check]