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 CDbundle. A CD costs $15. A deluxe CD bundle costs the same as one CD and one premium CD bundle. The band sells 400 CDs, 95 premium CDbundles, and 38 deluxe CD bundles for a total of $12,555. Find the price of each optionA CD costs $a premium CD bundle costs $and a deluxe CD bundle costs $

Answer 1

The cost of a CD is $ 15.

The cost of deluxe CD bundle=one CD+Premium CD bundle.

Let the cost on premium CD bundle is x and the cost of deluxe CD bundle is y.

The form the above relation,

y=15+x......(1)

The band sells 400 CDs, 95 premium CD and 38 deluxe CD bundles with total price of $ 12,555.

Then,

`\begin{gathered} 400*15+95(x)+38(y)=12555 \\ 6000+95x+38(15+x)=12555 \\ 95x+570+38x=12555-6000 \\ 133x=5985 \\ x=45 \end{gathered}`

The value of y can be determined as,

`\begin{gathered} y=15+45 \\ =60 \end{gathered}`

Thus, the cost of one CD is $ 15, the cost of premium CD bundle is $ 45, and the cost of deluxe CD bundle is $ 60.