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Rate problem

by datonman » Wed Nov 12, 2014 12:56 pm
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
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by [email protected] » Wed Nov 12, 2014 8:27 pm
Hi datonman,

This question can be solved in a couple of different ways, but it's perfect for TESTing VALUES.

We're told that X > Y so let's use:

X = 3 cents for the first pound
Y = 2 cents for each additional pound

With these numbers....
A 3-pound package would cost 3 + 2(2) = 7 cents
A 5-pound package would cost 3 + 4(2) = 11 cents

An 8-pound package would cost 3 + 7(2) = 17 cents

So mailing them separately costs 18 cents total, while mailing them combined costs 17 cents total.

We're asked which option would be cheaper and by how much. We know that mailing the packages combined is cheaper, so we just need to plug in X = 3 and Y = 2 into the first 3 answers and confirm that only one of them gives us an answer of 1 cent...

Final Answer: A

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Rich
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by Mathsbuddy » Fri Nov 14, 2014 6:33 am
Package A: 3 lb = 1 lb + 2 lb, so cost A = x + 2y
Package B: 5 lb = 1 lb + 4 lb, so cost B = x + 4y

Therefore Separately, cost S = A + B = 2x + 6y

Combined: 8 lb = 1 lb + 7 lb, cost C = x + 7y

As x > y, we could say that x = y + t (where x,y,t > 0)

So, S = 2(y + t) + 6y = 8y + 2t
and C = y + t + 7y = 8y + t

Therefore C < S with difference = t = x - y
So COMBINED is cheaper by (x - y)
Answer A.
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