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Sarah went to an electronics store, purchased 3 CDs and 5 DVDs, and spent $137. Michelle went to the same store, bought 2 CDs and 7 DVDs, and spent $161. How much does each CD sell for at the store? . . a) $13 . . b)$14 . . c)$18 . . d) $19 . .

Answer :

C. thats the only one that will give you the same price for the DVDS as well. they charge $14 for CDS and $19 for DVDS

Answer:

b) $14

Step-by-step explanation:

Let x be the cost of each CD and y be the cost of each DVD,

Since, 3 CDs and 5 DVDs cost $ 137,

⇒ 3x + 5y = 137 -------(1),

Also, 2 CDS and 7 DVDs cost $ 161,

⇒ 2x + 7y = 161 --------(2),

7 × equation (1) - 5 × equation (2)   ( ∵ we need the value of x so we have to eliminate y for this LCM(7,5) = 35 )

We get,

21x - 10x = 959 - 805

11x = 154

⇒ x = [tex]\frac{154}{11}[/tex] = 14

Hence, the cost of each CD is $ 14,

Option 'b' is correct.

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