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Movie Mania requires customers to pay a sign-up fee of $20, and charges $4.00 to rent a DVD. Hurricane Video is free to join, but DVDs cost $6.00 to rent. Write and solve an equation to find the number of DVDs you would have to rent in order for both stores to charge the same. Explain what your variable represents.Movie Mania requires customers to pay a sign-up fee of $20, and charges $4.00 to rent a DVD. Hurricane Video is free to join, but DVDs cost $6.00 to rent. Write and solve an equation to find the number of DVDs you would have to rent in order for both stores to charge the same. Explain what your variable represents.

Respuesta :

Answer:

10

Step-by-step explanation:

For movie mania:

Sign-up fee = $ 20

Rent for 1 DVD = $ 4.00

For Hurricane video:

Sign-up fee = 0

Rent of 1 DVD = $ 6.

Let [tex]n[/tex] be the number of DVDs to rent in order for both stores to charge the same.

For movie mania, charge to rent [tex]n[/tex] DVDs = Sign-up fee + rent of [tex]n[/tex] DVDs

=20+4n

For Hurricane movie, charge to rent [tex]n[/tex] DVDs = Sign-up fee + rent of [tex]n[/tex] DVDs

=0+6n=6n

Now, for both stores to charge the same, both the charges must be equal, we have

6n=20+4n

[tex]\Rightarrow 6n-4n=20[/tex]

[tex]\Righatarroe 2n=20[/tex]

[tex]\Rightarrow n =20/2=10[/tex]

Hence, the required number of DVDs to rent is 10 in order for both stores to charge the same.

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