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

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 $p$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):

$f=1.25$

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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):

$p=6.5$

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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!