Mozart's Music Store rents trombones for $34 a month. Bach's Music Store rents trombones for $30 per month plus a yearly fee of $48. Which deal is better if you plan to rent a trombone for 9 years (108 months)?

Let [tex]M(x)[/tex] be the cost of renting from Mozart's Music Store for [tex]x[/tex] years, and [tex]B(x)[/tex] be the cost of renting from Bach's Music Store for [tex]x[/tex] years.

From the problem statement, we can come up with the following equations:

[tex]M(x) = 34(12x)[/tex]

[tex]B(x) = 30(12x) + 48x [/tex]

Plugging in [tex]x = 9[/tex] for each equation, we can get the answer:

[tex]M(9) = 34(12 * 9)[/tex]

[tex]M(9) = 34(108)[/tex]

[tex]M(9) = 3672[/tex]

[tex]B(9) = 30(12 * 9) + 48(9)[/tex]

[tex]B(9) = 30(108) + 432[/tex]

[tex]B(9) = 3240 + 432[/tex]

[tex]B(9) = 3672[/tex]

From this, we can see that the value is equal for both stores.