A pottery studio gives two​-hour and ​four-hour ceramics classes for ​$43 an hour. If the studio has collected ​$4214 for a total of 36 ​classes, how many ​two-hour classes and how many four​-hour...

Question

A pottery studio gives two​-hour and ​four-hour ceramics classes for ​$43 an hour. If the studio has collected ​$4214 for a total of 36 ​classes, how many ​two-hour classes and how many four​-hour classes were paid​ for?

Blank two-hour classes (integer or decimal)

Blank four-hour classes (integer or decimal)

Answer 1

Here are two types of classes -One is a 2-hour clas and the other 4-hour class.

Suppose, number of 2-hour classes = x, and the number of 4-hour classes = y

since there are total 36 classes, we can write x + y=36 - - - - - - - - - (1)

As x is a 2-hour class x collects 2x43=86 in one class and y collects 4x43 = 172 in ane class.

during these classes total collected amount is 4214.

so that 86x + 172y = 4214 - - - - - (2)

Solving equations (1) and (2) by substitution method,

86(36-y) + 172y = 4214

or, 3096 - 86y + 172 y =4214

or, 86y=1118

y=13,

substituting the value of y in equation (1) x + 13 =36 , or x = 36 - 13 = 23

hence there 23 two hour classes and 13 four hour classes.

We can check the answer as, 23 x2($ 43) = $ 1978

13x4($ 43) = $ 2236

total collected amount = 4 4214

Answer 2

4214/43 =98 hours of classes

4x + 2(36-x) = 98

4x -2x = 98 -72

2x = 26

x = 13 four hour classes

36-13 = 23 two hour classes

43(13x4) + 43(23x2) = 43(52+46) = 43(98) = 4214