a pottery studio gives three-hour and five-hour classes for $41.00 an hour. The studio collects 6,437 for 41 classes. How many 3 hour classes and how many five hour classes were paid for?
X 3-hour classes.
(41-x) 5-hour classes.
41(3x) + 41*5(41-x) = $6,437.
123x + 8405-205x = 6,437
-82x = 6437-8405 = -1968
X = 24 3-hour classes.
41-x = 41-24 = 17 5-hour classes.
To solve this problem, we need to find out how many three-hour and five-hour classes were paid for by the studio.
Let's assume the number of three-hour classes is 'x' and the number of five-hour classes is 'y'.
Given that the studio charges $41.00 per hour and collected a total of $6,437.00 for 41 classes, we can set up two equations based on the information:
1) 3x + 5y = 6,437 (since x represents the number of three-hour classes and y represents the number of five-hour classes, we multiply 3 by x and 5 by y)
2) x + y = 41 (since there are a total of 41 classes)
Now, we have a system of two equations that we can solve simultaneously.
We can use the substitution method to solve the system:
From equation 2), we can express x in terms of y: x = 41 - y
Substituting this value of x in equation 1), we have: 3(41 - y) + 5y = 6,437
Expanding the equation, we get: 123 - 3y + 5y = 6,437
Combining like terms, we have: 2y = 6,437 - 123
Simplifying further, we get: 2y = 6,314
Dividing both sides by 2, we find: y = 6,314 / 2 = 3,157
So, the number of five-hour classes (y) is 3,157.
Now we can substitute this value of y back into equation 2) to find x:
x + y = 41
x + 3,157 = 41
Subtracting 3,157 from both sides, we have: x = 41 - 3,157 = -3,116
The result, -3,116, doesn't make sense in this context since we cannot have a negative number of classes. This means that there was an error in our calculations or assumptions.
Please double-check the given information or let me know if there is any missing context or if you notice any inconsistencies.
number of 3-hour classes --- x
number of 5-hour classes --- y
x+y = 41 ----> y = 41-x
3(41)x + 5(41)y = 6437
3x + 5y = 157
sub in the 1st equation ...
3x + 5(41-x) = 157
3x + 205 - 5x = 157
-2x = -48
x = 24
then y = 41-24 = 17
they sold 24 three-hour courses and
17 five-hour courses