SOLUTION: The fun guys game rental store chargesan annual fee of $10 plus $3.50 per game rented. The game bank the annual fee of $22 plus $2.50 per game. For how many game rentals will the c

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The fun guys game rental store chargesan annual fee of $10 plus $3.50 per game rented. The game bank the annual fee of $22 plus $2.50 per game. For how many game rentals will the c      Log On


   

Question 242798: The fun guys game rental store chargesan annual fee of $10 plus $3.50 per game rented. The game bank the annual fee of $22 plus $2.50 per game. For how many game rentals will the cost be the same at both stores? What is the cost?
Found 2 solutions by stanbon, oberobic:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The fun guys game rental store charges an annual fee of $10 plus $3.50 per game rented. The game bank the annual fee of $22 plus $2.50 per game. For how many game rentals will the cost be the same at both stores? What is the cost?
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Fun Cost: F(x) = 10 + 3.5x
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Game Cost: G(x) = 22 + 2.5x
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Equation:
10 + 3.5x = 22 + 2.5x
x = 12 (Cost will be the same at both stores when x = 12)
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The cost will be 10 + 3.5*12 = $52.00
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Cheers,
Stan H.

Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
Define your terms:
x = number of game bank rentals
f = cost of fun guys game rentals = $10 + $3.50 * x = 10 + 3.5x.
g = cost of game bank rentals = $22 + $2.50 * x = 22 + 2.5x.
The question actually asks 2 questions
1) What value of x makes the costs the same?
2) What is the cost?
Answering questions:
To test the value of x that makes the costs equal, set the equations equal to one another.
10 + 3.5x = 22 + 2.5x
Subtracting 2.5x from both sides.
10 + 1x = 22. (Note that 1x is typically shown as just 'x'.)
Subtracting 10 from both sides.
x = 22 - 10 = 12.
Check your work by substituting in for values you don't know.
f = 10 + 3.5(12) = 10 + 42 = 52
g = 22 + 2.5(12) = 22 + 30 = 52
That shows the value x = 12 solves both.
And checking the solutions reveals the answer to the second question: $52.
An interesting third question is: Which is the better value?
Since the annual dues are paid just once, after you rent at least 12 games per year, the game bank is cheaper per rental: $2.50 vs. the $3.50 charged by the fun guys.
So, IF you plan to rent at least 12 games per year (or 1 per month), then the game bank is less costly.