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saw5 [17]
3 years ago
10

You and your friend each purchased identical subscriptions to an online video rental site. When you joined, you each paid the on

e-time membership processing fee. You also paid a flat rate for each movie that you downloaded. By the end of the first month, you had downloaded 8 movies and paid $16.50, while your friend had downloaded only 6 movies and paid $14.00. What was the amount of the flat fee you paid?
Mathematics
1 answer:
nikitadnepr [17]3 years ago
4 0

Answer:

$1.25

Step-by-step explanation:

Let f equal the flat rate.

Let p equal the one-time membership processing fee.

Start with a system of equations:

16.50=8f+p

14=6f+p

Use the elimination method and multiply your second equation by -1 to cancel out the ps:

-1(14=6f+p)

Now combine the equations:

16.50=8f+p

-14=-6f-p

Subtract:

2.5=2f

Divide by the coefficient of f, which is 2 (I rearranged the equation):

f=1.25

~

Even though we're not solving for the one-time processing fee, to check our work, we'll need to solve for p, so start with the initial system of equations:

16.50=8f+p

14=6f+p

Use the elimination method and multiply the first equation by 3, and the second equation by -4:

3(16.50=8f+p)

-4(14=6f+p)

Multiply:

49.50=24f+3p

-56=-24f-4p

Subtract:

-6.5=-p

Divide by the coefficient of p, which is -1 (Rearranged equation):

p=6.5

~

Check your work:

16.50=8(1.25)+6.5

14=6(1.25)+6.5

Solve:

16.50=16.50

14=14

It's correct!

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