Question

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

Answer 1

$1.25

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
`p`s:

`-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!