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These are the fees for sending a package by Media Mail:

$\bullet$ $\$2.41$ for the first pound

$\bullet$ $\$0.41$ per additional pound for the next six pounds

$\bullet$ $\$0.39$ per additional pound after that

For example, a two-pound package costs $\$2.82$ to send by Media Mail.

If a package full of books costs $\$7.99$ to send by Media Mail, how many pounds does the package weigh? Explain your work in complete sentences.

Formatting tip: To write a dollar sign, use $\verb#\$#$. If you use just $, the homework system will think that is $\LaTeX$. Please review your solution for formatting problems.

Respuesta :

First pound costs = [tex] $\verb#$2.41#$ [/tex]

Next 6 pound costs = [tex] $\verb#$0.41#$ [/tex] * 6 = [tex] $\verb#$2.46#$ [/tex]

cost per additional pound is [tex] $\verb#$0.39#$ [/tex] after 7 pounds.

Let x be the weight of package in pounds

additional pound is (x-7)

Cost of package = cost of 1 pound + cost of 6 pounds + cost of additional pounds

Given cost of package = 7.99

Cost =[tex] 2.41 + 2.46 + 0.39 (x-7) [/tex]

[tex] 7.99 = 2.41 + 2.46 + 0.39 (x-7) [/tex]

[tex] 7.99 = 4.87 + 0.39 (x-7) [/tex]

Subtract 4.87 on both sides

[tex] 3.12 = 0.39x - 2.73 [/tex]

Add 2.73 on both sides

[tex] 5.85 = 0.39 x [/tex]

Divide by 0.39 on both sides

[tex] x = 15 [/tex]

The package weight 15 pounds


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