Question

There are three options for fans purchasing a band's new release CD. They can purchase the CD, a premium CD bundle, or a deluxe CD bundle. A CD costs $10. A deluxe CD bundle costs the same as 2 CDs and one premium CD bundle. The band sells 450 CDs, 110 premium CD bundles, and 45 deluxe CD bundles for a total of $11,600. Find the price of each option.

Answer 1

The price of each CD is $10, the price of each premium CD bundle is $40 and the price of each deluxe CD bundle is $60.

Equation

An equation is an expression used to show the relationship between one or more numbers and variables.

Let x represent the price of a premium CD bundle and y represent the price of a deluxe CD bundle. The price of a CD is $10. Hence:

y = 2(10) + x

-x + y = 20    (1)

Also:

450(10) + 110x + 45y = 11600

110x + 45y = 7100  (2)

From equation 1 and 2:

x = 40, y = 60

The price of each CD is $10, the price of each premium CD bundle is $40 and the price of each deluxe CD bundle is $60.

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