SOLUTION: Define variables and write a system of equations for each situation. Solve by using substitution. Suppose you want to join a video store. Big Video offers a special discount ca

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Question 30452: Define variables and write a system of equations for each situation. Solve by using substitution.
Suppose you want to join a video store. Big Video offers a special discount card that costs $9.99 for one year. With the discount card, each video rental costs $2.49. A discount card from Main Street Video cost $20.49 for one year. With the Main Street Video discout card, each video rental costs $1.79. After how many video rentals is the cost the same?
Found 2 solutions by mbarugel, josmiceli:
Answer by mbarugel(146) (Show Source):
You can put this solution on YOUR website!
Let's call X to the number of video rentals you make.
If you go with the Big Video card, your total cost will be:

If you go with Main Street video card, your total cost will be:

So the system of equations is:

Substituting the 2nd equation into the 1st one, we get:

The cost will be the same after 15 video rentals.

Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
Big Video has a flat rate of $9.99/yr + $2.49/rentalo
Main Video has a flat rate of $20.49/yr + $1.79/rental
Let y = cost of renting videos
Let x = number of videos rented
the equations for the first year in each case are

substitute y in the first equation for y in the 2nd

subtract 9.99 from both sides

subtract 1.79*x from both sides

What that says is, assuming that the rentals from both
stores are all done in the first year, after 15 rentals
from each, the cost of renting is the same at each store
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There are 4 possibilities, however
[1] rentals from both stores are in the same year
[2] rentals from both stores spill over into the next year
[3] rentals from Big Video only spill over into next year
[4] rental from Main St Video only spill over into next year
The statement of the problem sounds like the video rentals are
in the same time period, so I'll eliminate cases [3] & [4],
but to cover case [2], I write new equations
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I doubled the flat yearly cost for each store

So it would take 30 rentals for the costs to be equal if all the
rentals did not occur in the 1st year
I think it's kind of a trick question
Here are graphs that illustrate cases [1] & [2]

to check solutions, case [1]

costs are equal as they should be
checking case [2]

costs are equal