A pottery studio gives 3 hour and five hour classes for $37 an hour. If the studio has collected $4810 for a total of 28 classes, how many two hour classes an

Question

A pottery studio gives three hour and five hour cereamic classes for $37 an hour. If the studio has collected $4810 for a total of 28 classes, how many three hour classes and how many five hour classes were paid for?

Answer 1

Your best bet would be to break it down as

 

185x + 111y = 4810

 

where 185x would be the total cost of 5 hr classes and 111y would be the amount for the 3 hr classes

 

 

 

 

Answer 2

4810 / 37 = 130 hours

let r = three-hour classes and f = 5-hour classes

Here's what we know:

r + f = 28 (the number of the two classes is 28)

3r + 5f = 130 (hours spent is 130)

 

We have our choice of isolating a variable and using substitution, or we can multiply the first equation by -3 or -5 and use elimination. I'll use the latter:

-3r - 3f = -84

3r + 5f = 130

-------------------

2f = 46

f = 23

 

r + 23 = 28

r = 5

 

Check:

3 * 5 + 5 * 23 = 130

15 + 115 = 130

130 = 130