A pottery studio gives three-hour and four-hour ceramics classes for $34 an hour. If the studio has collected $2958 for a total of 27 classes, How many three-hour classes and four-hour classes were...

Question

paid for?

Blank three-hour classes (Type an integer or a decimal)

Blank four-hour classes (Type an integer or a decimal)

Answer 1

Let X be the number of 3 hour classes and Y the number of 4 hour classes.

We know that X + Y = 27 classes total.

Since each class has the same rate of $34/hour, we can find the total charge for each class:

X (3 hr classes) = 3*($34/hour) = $102/class

Y (4 hr. classes) = 4*($34/hour) = $136/class

The total income for 27 classes is $2958. This would be composed of the numbers of 3 and 4 hours classes times the fee for that class:

X: ($102/class)*(X classes)

Y ($136/class)*(Y classes)

Putting these into one equation:

102X + 136Y = 2958

We can use a definition of X by rearranging the first equation:

X + Y = 27 classes total

X = (27 - Y)

Put this into the second equation:

102X + 136Y = 2958

102*(27 - Y) + 136Y = 2958

2754 - 102Y + 136Y = 2958

34Y = 204

Y = 6

Since X = (27 - Y)

X = (27-6)

X = 21

There are 21 3 hr classes, and

6 4 hr classes

That is a total of 27 classes.

The income from these numbers is:

21*($102/class) = $2142

6*($136/class) = $ 816

$2958

Answer 2

x = number of 3 hour classes

27-x = number of 4 hour classes

cost of 3 hour classes = 3*34*x = 102x

cost of 4 hour classes = 4*34*(27-x) = 136(27-x) = 3672 - 136x

total cost = 2958

102x + 3672 - 136x = 2958

-34x = -714

x = 21

21 3 hour classes

27-21 = 6 4 hour classes

Answer 3

Let t be the number of three hour classes and f be the number of four hour classes.

t+f = 27 Equation 1

34(3t)+34(4f)=$2958

Divide both sides by 34

3t+4f = 87 Equation 2

Subtracting 3 times equation 1 from equation 2:

3t + 4f = 87

-3t - 3f = -81

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

f = 6

t + 6 =27 --> t = 21

21 three-hour classes

6 four-hour classes