swerve wrote: ↑

Wed Dec 02, 2020 10:06 am

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 separately or combined as one package. Which method is cheaper, and how much money is saved?

A. Combined, with a savings of \(x-y\) cents
B. Combined, with a savings of \(y-x\) cents
C. Combined, with a savings of \(x\) cents
D. Separately, with a savings of \(x-y\) cents
E. Separately, with a savings of \(y\) cents

The OA is A

Source: Official Guide

Solution:

We can solve this problem by first creating expressions for the given information. We know that the rate is x cents for the first pound and y cents for each pound after the first. This can be written as:

x + y(t – 1), in which t is the number of pounds of the package. Let’s first determine the cost of mailing the two packages separately. We start with the 3-pound package:

x + y(3 – 1)

x + y(2)

x + 2y

Next we can determine the cost of mailing the 5-pound package:

x + y(5 – 1)

x + y(4)

x + 4y

Thus, the total cost of mailing the two individual packages separately is:

x + 2y + x + 4y = 2x + 6y

Now let's determine the cost of mailing the two packages if they are combined as one package. The combined package would weigh 8 pounds, and its shipping cost would be:

x + y(8 – 1)

x + y(7)

x + 7y

We are given that x > y, and so we see that mailing the packages individually is more costly than mailing them as one combined package. We now need to determine the difference in cost between the two mailing options:

2x + 6y – (x + 7y)

2x + 6y – x – 7y

x – y

Thus, the savings is (x – y) cents when the packages are shipped as one combined package.

Answer: A