a pottery studio gives three hour and four-hour classes for $48 an hour. If the studio has collected $8592 for a total of 50 classes how many three-hour classes

Question

a pottery studio gives three hour and four-hour classes for $48 an hour. If the studio has collected $8592 for a total of 50 classes how many three-hour classes and four-hour classes where paid for

Answer 1

Let's first change the money into hours: $8592 / $48 per hour = 179 hours total. 

 

If all 50 classes were 3-hour ones, we will end up with 50 * 3 = 150 hours.

 

In reality, 50 classes have 179 - 150 = 29 hours more than the above situation because some classes were 4-hours. 

 

The number of classes that were 4-hours was 29, to bring up the total hours to 179.

 

We have 29 4-hour classes, 3-hour classes are 50 - 29 = 21. 

Answer 2

Let x be the number of 3-hour lessons, and y be the number of 4-hour lessons.

We have x+y = 50 AND 48(3x+4y)=8592

so y = 50-x,

48[3x+4(50-x)]=8592

3x +200-4x = 179

-x = -21

x=21

 

y = 50-21 =29

 

so 21 3-hr lessons and 29 4hr lessons.

 

 

Answer 3

This problem is all about ratios.  You can solve by trial and error, which may be a simple way to understand it.

 

First, calculate the total amount for the 3-hour and 4-hour classes -

3-hour class: $48 x 3 hours = $144

4-hour class: $48 x 4 hours = $192

 

Next, use trial and error - 

Suppose, 25 classes of each hour were were given.  It would look like this

25 3-hour classes:  25 x $144 = $4800

25 4-hour classes:  25 x $192 = $3600

 

Add the total:  $4800 + $3600 = $8400

That's not quite $8592.  Therefore, you will have to assume that there were more 4-hour classes given.

 

Let's try 30 4-hour classes and 20 3-hour classes -

20 3-hour classes:  20 x $144 = $2880

30 4-hour classes:  30 x $192 = $5760

 

Add the total:  $2880 + $5760 = $8640. 

Now, we're way over the amount of 4-hour classes that were given.  You can see now that your magic number of 4-hour classes is between 25 and 30 classes. 

 

Let's try 29 4-hour classes and 21 3-hour classes -

21 3-hour classes:  21 x $144 = $3024

29 4-hour classes:  29 x $192 = $5568

 

Add the total:  $3024 + $5568 = $8592

 

Therefore, 21 3-hour classes and 29 4-hour classes were paid for at the pottery studio.