Question

To mail a package, the rate is x cents for the first pound and y cents for each additional pound, where x>y. Two packages weighing 3 pounds and 5 pounds, respectively can be mailed seperately or combined as one package. Which method is cheaper and how much money is saved?A. Combined, with a saving of x-y centsB. Combined, with a saving of y-x centsC. Combined, with a saving of x centsD. Separately, with a saving of x-y centsE. Separately, with a saving of y cents

Answer 1

Option A) Combined, with a saving of x-y cents

Explanation:

We are given the following in the question:

The rate to mail a package is x cents for first pound and y cents for each additional pound.

`x>y`

Weights of packages =

3 pounds and 5 pounds

Cost of combined package:

Total weight = 8 pounds

`C\text{(combined)} = x + 7y`

Cost of sending separately:

`C\text{(separated)} = (x + 2y) + (x + 4y) = 2x + 6y`

Difference between cost of sending the packages separately and combined

`C\text{(separated)}-C\text{(combined)} \\=2x + 6y-(x+7y)\\=(x-y)\text{ cents}`

Thus, sending the packages combined is a cheaper method with a saving of (x-y) cents

Thus, the correct answer is:

Option A) Combined, with a saving of (x-y) cents