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To mail a package, the rate is x cents for the first pound [#permalink]

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17 Dec 2012, 06:37

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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

Re: To mail a package, the rate is x cents for the first pound [#permalink]

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17 Dec 2012, 06:40

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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.

Re: To mail a package, the rate is x cents for the first pound [#permalink]

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09 Jan 2013, 21:22

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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.

Re: To mail a package, the rate is x cents for the first pound [#permalink]

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11 Mar 2013, 20:52

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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) _________________

Re: To mail a package, the rate is x cents for the first pound [#permalink]

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10 Jan 2014, 02:38

Bunuel wrote:

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.

I came to this conclusion: \((2x+6y) = (x+7y)\), but obviously nothing tells us that posting in one 8 pound package is EQUAL to posting separately, actually the question even implies there's a difference.. But anyways, my calculations with the above in mind ended up in: \((x+7y) - (2x+6y) = y - x\), so I went with B

My question is: For questions like these, what is it that makes you "know" that the difference we are supposed to calculate is Separately - Together? That subtraction is not very immediately intuitive to me, why would we for instance not go the other way: Together - Separately?

Re: To mail a package, the rate is x cents for the first pound [#permalink]

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10 Jan 2014, 03:19

Expert's post

aeglorre wrote:

Bunuel wrote:

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.

I came to this conclusion: \((2x+6y) = (x+7y)\), but obviously nothing tells us that posting in one 8 pound package is EQUAL to posting separately, actually the question even implies there's a difference.. But anyways, my calculations with the above in mind ended up in: \((x+7y) - (2x+6y) = y - x\), so I went with B

My question is: For questions like these, what is it that makes you "know" that the difference we are supposed to calculate is Separately - Together? That subtraction is not very immediately intuitive to me, why would we for instance not go the other way: Together - Separately?

Thank you

Please read the red part in the solution you are quoting.

Re: To mail a package, the rate is x cents for the first pound [#permalink]

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12 Jan 2014, 20:57

Expert's post

aeglorre wrote:

I came to this conclusion: \((2x+6y) = (x+7y)\), but obviously nothing tells us that posting in one 8 pound package is EQUAL to posting separately, actually the question even implies there's a difference.. But anyways, my calculations with the above in mind ended up in: \((x+7y) - (2x+6y) = y - x\), so I went with B

My question is: For questions like these, what is it that makes you "know" that the difference we are supposed to calculate is Separately - Together? That subtraction is not very immediately intuitive to me, why would we for instance not go the other way: Together - Separately?

Thank you

I would like to further point out here that since you are given that x > y, when you get the answer as y - x, you should realize that this will be negative. But money saved must be positive so Separately must be higher than Together and you are required to find Separately - Together. Also, Separately = 2x + 6y Together = x + 7y Separately has an x instead of a y and since x is higher, Separately is higher than Together. _________________

Re: To mail a package, the rate is x cents for the first pound [#permalink]

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30 May 2015, 06:00

Together: x + 7y Separately: x + 2y + y + 4y = 2x + 6y to send the package together will be cheaper because x>y (If Separately we have one x more and one y less, but we know that x>y) --> 2x+6y - x -7y = x-y (A) _________________

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