Question

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.

Answer 1

First pound costs =
`$\verb#$2.41#$`

Next 6 pound costs =
`$\verb#$0.41#$` * 6 =
`$\verb#$2.46#$`

cost per additional pound is
`$\verb#$0.39#$` 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 =
`2.41 + 2.46 + 0.39 (x-7)`

`7.99 = 2.41 + 2.46 + 0.39 (x-7)`

`7.99 = 4.87 + 0.39 (x-7)`

Subtract 4.87 on both sides

`3.12 = 0.39x - 2.73`

Add 2.73 on both sides

`5.85 = 0.39 x`

Divide by 0.39 on both sides

`x = 15`

The package weight 15 pounds