CDs and DVDs Solve by setting up a system of linear equations with 2 variables and 2 unknowns. CDs cost $5.96 more than DVDs at All Bets Are Off Electronics. How much would 6 CDs and 2 DVDs cost if 5 CDs and 2 DVDs cost $127.73?

Question

Mathematics

Demetrius Avila

29 January, 04:16

CDs and DVDs Solve by setting up a system of linear equations with 2 variables and 2 unknowns. CDs cost $5.96 more than DVDs at All Bets Are Off Electronics. How much would 6 CDs and 2 DVDs cost if 5 CDs and 2 DVDs cost $127.73?

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Answers (1)

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Reuben Jones · Answer 1

6 CDs and 2 DVDs would cost $147.68.

Let c be the cost of a CD and d be the cost of a DVD.

We know that c = d+5.96.

We also know that 5c+2d = 127.73.

Substituting our value of c from the first equation into the second one, we have

5 (d+5.96) + 2d = 127.73

Using the distributive property,

5*d+5*5.96+2d = 127.73

5d+29.80+2d = 127.73

Combining like terms,

7d+29.80 = 127.73

Subtract 29.80 from both sides:

7d+29.80-29.80=127.73-29.80

7d = 97.93

Divide both sides by 7:

7d/7 = 97.93/7

d = 13.99

c = d + 5.96 = 13.99+5.96 = 19.95

6 CDs and 2 DVDs would be

6 (19.95) + 2 (13.99) = 147.68