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 $15. a deluxe cd bundle costs the same as one cd and 2 premium cd bundles. the band sells 455 cds, 87 premium cd bundles, and 35 deluxe cd bundles for a total of $12,845. find the price of each option.

The price of CD's = $15

The price of deluxe bundles  = $85

The price of premium bundles. = $ 35

Step-by-step explanation:

Let c represents the number of CD's

Let d represents the number of deluxe bundles

Let p represents the number of premium bundles.

Now according to the given statement:

c = $15

d = c+2p =

d = 15+2p equation 1

455c+87p+35d = $12,845 equation 2

Now substitute the value of d in equation 2 to find the value of p

455c+87p+35d = $12,845

455(15)+87p+35(15+2p) = $12,845

6825+87p+525+70p=$12,845

Now combine the like terms:

6825+157p+525 = $12,845

Now shift all the like terms to the R.H.S

157p= 12845-6825-525

157p = 5495

Divide both sides by 157

157p/157 = 5495/157

p = 35

Now substitute the value p =35 in equation 1.

d = 15+ 2p

d = 15+2(35)

d = 15+70

d = 85

Therefore we have found that,

The price of CD's = $15

The price of deluxe bundles  = $85

The price of premium bundles. = $ 35

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