Carcass wrote:
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
To mail a package, the rate is x cents for the first pound and y cents for each additional pound, where x > y.Cost of 3-pound packageWe pay x cents for the first pound, and then y cents for each of the 2 additional pounds.
Total cost = x + y + y =
x + 2yCost of 5-pound packageWe pay x cents for the first pound, and then y cents for each of the 4 additional pounds.
Total cost = x + y + y + y + y =
x + 4yTOTAL cost = (
x + 2y) + (
x + 4y) =
2x + 6y-------------------------
Now let's see what happens when we COMBINE the two packages into an 8-pound package
Cost of 8-pound packageWe pay x cents for the first pound, and then y cents for each of the 2 additional pounds.
Total cost = x + y + y + y + y + y + y + y =
x + 7y-------------------------
Which method is cheaper, and how much money is saved?We must determine which value is less:
2x + 6y or
x + 7yWe're told that
x > y. So let's use this information.
Take:
2x + 6y and rewrite it as
(x + 6y) + xTake:
x + 7y and rewrite it as
(x + 6y) + yBoth quantities have (x + 6y) in common. So those values are equal.
Since
x > y, we know that
(x + 6y) + y is
less than (x + 6y) + xIn other words,
x + 7y is
less than 2x + 6yIn other words, the packages COMBINED is the cheaper option.
Determine the savings, we'll subtract the cheaper cost from the more expensive cost.
In other words: savings = (
2x + 6y) - (
x + 7y) = x - y (cents)
Answer: A
Cheers,
Brent
_________________
Brent Hanneson - founder of Greenlight Test Prep