Define variables and write a system of equations for this situation. Solve 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 costs $20.49 for one year. With the Main Street Video discount card, each video rental costs $1.79. After how many video rentals is the cost the same?
Cost of x videos from Big Video:
9.99 + 2.49x
Cost of x videos from Main Street Video:
20.49 + 1.79x
Set the two equations equal to each other to find when the cost will be the same:
9.99 + 2.49x = 20.49 + 1.79x
10.5 = .7x
x = 15 videos
i see..
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To define the variables, let's consider the following:
Let x be the number of video rentals.
Let C1 be the total cost when using the Big Video discount card.
Let C2 be the total cost when using the Main Street Video discount card.
With this information, we can write the system of equations as follows:
C1 = 9.99 + 2.49x (Total cost with Big Video card)
C2 = 20.49 + 1.79x (Total cost with Main Street Video card)
To solve the system using substitution, we need to find the point of intersection where C1 and C2 are equal. So we equate the two equations:
9.99 + 2.49x = 20.49 + 1.79x
Now, let's solve for x:
Add -1.79x to both sides of the equation:
9.99 + 2.49x - 1.79x = 20.49 + 1.79x - 1.79x
Combine like terms:
9.99 + 0.7x = 20.49
Subtract 9.99 from both sides of the equation:
9.99 + 0.7x - 9.99 = 20.49 - 9.99
Simplify:
0.7x = 10.5
Now, divide both sides of the equation by 0.7 to solve for x:
(0.7x) / 0.7 = 10.5 / 0.7
Simplify:
x = 15
Therefore, the cost will be the same after renting 15 videos.