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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

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.

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]

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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?

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.

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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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

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), where t is the number of pounds of the package. Let’s first determine the cost of mailing the two individual 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 for the two individual packages (if they are mailed separately) is:

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

Now let's determine the cost of 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
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