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To mail a package, the rate is x cents for the first pound [#permalink]
 17 Dec 2012, 06:37
Question Stats:
60% (02:01) correct
40% (01:00) wrong based on 9 sessions
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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Re: To mail a package, the rate is x cents for the first pound [#permalink]
17 Dec 2012, 06:40
Walkabout 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 Shipping separately costs 1x+2y for the 3 pounds package (x cents for the first pound and y cents for the additional 2 pounds) plus 1x+4y for the 5 pounds package (x cents for the first pound and y cents for the additional 4 pounds), so total cost of shipping separately is (x+2y)+(x+4y)=2x+6y; Shipping together in one 8-pound package costs 1x+7y (x cents for the first pound and y cents for the additional 7 pounds); Difference: Separately-Together=(2x+6y)-(x+7y)=x-y --> as given that x>y then this difference is positive, which makes shipping together cheaper by x-y cents. Answer: A. Hope it's clear.
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Re: To mail a package, the rate is x cents for the first pound [#permalink]
09 Jan 2013, 21:22
Walkabout 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 Back solve and plug in numbers: x>y x=4 y=3 A=3lbs, B=5lbs A=4+3*2=10 B=4+3*4=16 Individually =$26 Together=4+7*3=25 Combined is cheaper and by looking at the answers you can get $1 x-y Solved in 1min 45 secs so is approachable this way and may seem easier than algebraically, cheers. Answer:A
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Re: To mail a package, the rate is x cents for the first pound [#permalink]
13 Jan 2013, 23:54
The actual weight of the packages is irrelevant, so long as both weights are positive integers. Even if the packages weighed 1234 pounds and 5678 pounds, you would still get x-y as you are only saving on the first pound. No need to do any algebra, nor to plug in any numbers.
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Re: To mail a package, the rate is x cents for the first pound [#permalink]
11 Mar 2013, 18:06
For me, picking numbers helped the most and talking myself through this question.
x cents for the first pound and y cents for each additional pound
The rule is x>y
(obviously because usually when someone tries to give you a deal they say "buy this thing and get the 2nd thing for a cheaper amount!")
Pick some easy numbers:
x=10 cents
y=5 cents
Given: two packages that are 3 pounds and 5 pounds
Question: What method (combined or separately) is cheaper and how much is saved?
Sending out separate packages:
3 pound package:
1(first cent per pound x) + 2(additional cents per pound y)
1(10)+2(5) = 20
5 pound package:
1(first cent per pound x)+4(additional cents per pound y)
1(10)+4(5) = 30
30+20 = 50
Sending the two packages combined:
Two packages are: 3 pounds + 5 pounds = 8 pounds
8 pound package:
1(first cent per pound x)+7(additional cents per pound y)
1(10) + 7(5) = 45
What's cheaper and by how much?
We realize that the combined (45) is cheaper than the separate(50) package.
It's cheaper by 5 cents or x-y
Answer is A.
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Re: To mail a package, the rate is x cents for the first pound [#permalink]
11 Mar 2013, 20:52
DelSingh wrote: For me, picking numbers helped the most and talking myself through this question.
x cents for the first pound and y cents for each additional pound
The rule is x>y
(obviously because usually when someone tries to give you a deal they say "buy this thing and get the 2nd thing for a cheaper amount!")
Pick some easy numbers:
x=10 cents
y=5 cents
Given: two packages that are 3 pounds and 5 pounds
Question: What method (combined or separately) is cheaper and how much is saved?
Sending out separate packages:
3 pound package:
1(first cent per pound x) + 2(additional cents per pound y)
1(10)+2(5) = 20
5 pound package:
1(first cent per pound x)+4(additional cents per pound y)
1(10)+4(5) = 30
30+20 = 50
Sending the two packages combined:
Two packages are: 3 pounds + 5 pounds = 8 pounds
8 pound package:
1(first cent per pound x)+7(additional cents per pound y)
1(10) + 7(5) = 45
What's cheaper and by how much?
We realize that the combined (45) is cheaper than the separate(50) package.
It's cheaper by 5 cents or x-y
Answer is A. Number plugging is a great technique. Though, it will be good if you understand the logic too. You could save yourself some time and energy. Cost of first pound - x cents Cost of every additional pound - y cents x > y So first pound is costlier than every subsequent pound. Two packets - 3 pounds, 5 pounds If I have 8 pounds, I should send them together so that there is only one expensive 'first pound'. If I send them separately, I will have two expensive 'first pounds'. After putting 3 pounds in the packet, if I continue to put the 4th pound in the same packet, I save money on it because it is not the expensive 'first pound' which costs x cents but rather the fourth pound which costs only y cents. The rest of the 4 pounds go as the same y cents rate whether they are sent separately or together. So the only saving when I send them together is x - y on the fourth pound of the combined packet. Answer (A)
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Re: To mail a package, the rate is x cents for the first pound
[#permalink]
11 Mar 2013, 20:52
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