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

$2.41 for the first pound

$0.41 per additional pound for the next six pounds

$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?

Please help answer this thanks...

We would like to know which mailing rate(s) apply to our package. Since the mailing rate changes after the first 7 pounds, we start by considering the price to mail a 7-pound package. This price is $2.41 + 6 x (0.41) = $4.87. Since our package costs more than $4.87 to mail, we know it weighs more than 7 pounds. Specifically, our package costs $7.99 = 4.87 + 3.12, so the additional weight after the first 7 pounds accounts for $3.12 of the price. Since additional weight after the first 7 pounds is priced at $0.39 per pound, the additional weight of our package after the first 7 pounds must be 3.12 ÷ 0.39 = 8 pounds. Therefore, the total weight of the package is 7+8 = 15 pounds.

Solution #2

We start by making an educated guess. Shipping prices are approximately $0.40 per pound, plus a base charge of $2. Our package costs about $8 to mail, which is $6 more than the base charge. Since $0.40 goes into $6 fifteen times, we guess that the package weighs about 15 pounds. Remember, this is only an estimate! To find out if we're correct, we compute precisely how much a 15-pound package costs to ship.

Using the prices given in the problem, a 15-pound package costs $2.41 + 6(0.41) + 8(0.39) to ship. If you work this out, you will find that it is equal to $7.99. So, the weight of the package is indeed 15 pounds.