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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?

Respuesta :

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
MrRoyal

The relationship between the total cost and the costs of CDs and DVDs are represented by a linear function.

The cost of 6 CDs and 2 DVDs is $147.68

Let:

[tex]C \to CDs[/tex]

[tex]D \to DVDs[/tex]

From the question, we have:

[tex]C = D + 5.96[/tex]

[tex]5C + 2D = 127.73[/tex]

Substitute [tex]C = D + 5.96[/tex] in [tex]5C + 2D = 127.73[/tex]

[tex]5 \times (D + 5.96) + 2D = 127.73[/tex]

[tex]5D + 29.8 + 2D = 127.73[/tex]

Collect like terms

[tex]5D + 2D = 127.73 - 29.8[/tex]

[tex]7D = 97.93[/tex]

Divide both sides by 7

[tex]D = 13.99[/tex]

Substitute [tex]D = 13.99[/tex] in [tex]C = D + 5.96[/tex]

[tex]C = 13.99 + 5.96[/tex]

[tex]C = 19.95[/tex]

The cost of 6 CDs & 2 DVDs is represented as:

[tex]Cost =6C + 2D[/tex]

So, we have:

[tex]Cost =6 \times 19.95 + 2 \times 13.99[/tex]

[tex]Cost =147.68[/tex]

Hence, the cost of 6 CDs & 2 DVDs is $147.68

Read more about linear equations at:

https://brainly.com/question/11897796

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