Question 1201188: A fitness club charges members a monthly fee and a fee for each fitness class. Last month, one member attended 8 fitness classes and paid 80$. Another member attended 14 fitness classes and paid $98. Determine the monthly fee and the fee per class.
Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39613)   (Show Source):
You can put this solution on YOUR website! x, number of fitness classes
y, what member paid for the month
Two points (x,y):
(8,80) and (14,98).
Use them to find equation for the line. Take needed values asked from the slope-intercept form equation.
Answer by ikleyn(52752)  (Show Source):
You can put this solution on YOUR website! .
The difference in the number of classes 14-8 = 6 costs as much
as the difference of two total payments, i.e. 98-80 = 18 dollars.
Hence, each single class costs 18/6 = 3 dollars.
Thus fee per class is 3 dollars.
Then the monthly "flat" fee is 80-8*3 = 80-24 = 56 dollars. ANSWER
CHECK. The monthly "flat" fee, calculated by another way, is
98-3*14 = 98-42 = 56 dollars, i.e. the same amount.
Solved.
Answer by greenestamps(13195)  (Show Source):
You can put this solution on YOUR website!
The total cost is a flat fee plus a certain amount for each class, so the formula for the total cost is of the form
y = mx+b
where y is the total cost and x is the number of classes. The b is the flat fee (the total cost with 0 classes), and the m is the additional cost per class.
We have
80 = 8x+b
98 = 14x+b
Subtract the first equation from the second to find
18 = 6x
x = 18/6 = 3
The additional cost for each class is $3.
Use that result in either equation to find the flat fee:
80 = 8(3)+b
80 = 24+b
b = 80-24 = 56
The flat fee is $56
ANSWERS: $56 flat fee, $3 per class.
That is a formal algebraic solution, which is probably what you were looking for. However, that solution followed very formal process, in which you basically plugged numbers into standard equations to get the answer.
In my opinion, solving the problem using logical reasoning and simple arithmetic is a much better exercise for your brain.
So do as tutor @ikleyn suggests:
The 14-8 = 6 additional classes cost and additional $98-$80 = $18, so the cost per class was $18/6 = $3; then since the cost with 8 classes was $80, the flat fee is the $80-8($3) = $80-$24 = $56.
You do exactly the same arithmetic as with the formal algebraic solution -- but you get a much better understanding of HOW the problem is actually solved.
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