Daisycake1215
contestada

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?

Respuesta :

mastercookie55

Answer:

$1.25

Step-by-step explanation:

Let [tex]f[/tex] equal the flat rate.

Let [tex]p[/tex] equal the one-time membership processing fee.

Start with a system of equations:

[tex]16.50=8f+p[/tex]

[tex]14=6f+p[/tex]

Use the elimination method and multiply your second equation by [tex]-1[/tex] to cancel out the [tex]p[/tex]s:

[tex]-1(14=6f+p)[/tex]

Now combine the equations:

[tex]16.50=8f+p[/tex]

[tex]-14=-6f-p[/tex]

Subtract:

[tex]2.5=2f[/tex]

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

[tex]f=1.25[/tex]

~

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

[tex]16.50=8f+p[/tex]

[tex]14=6f+p[/tex]

Use the elimination method and multiply the first equation by [tex]3[/tex], and the second equation by [tex]-4[/tex]:

[tex]3(16.50=8f+p)[/tex]

[tex]-4(14=6f+p)[/tex]

Multiply:

[tex]49.50=24f+3p[/tex]

[tex]-56=-24f-4p[/tex]

Subtract:

[tex]-6.5=-p[/tex]

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

[tex]p=6.5[/tex]

~

Check your work:

[tex]16.50=8(1.25)+6.5[/tex]

[tex]14=6(1.25)+6.5[/tex]

Solve:

[tex]16.50=16.50[/tex]

[tex]14=14[/tex]

It's correct!

Otras preguntas