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? explain your work in complete sentences.

15 pounds

Step-by-step explanation:

We show two possible approaches.

Solution #1

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.