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

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

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25 Aug 2011, 09:02
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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 seperately or combined as one package. Which method is cheaper and how much money is saved?

A. Combined, with a saving of x-y cents
B. Combined, with a saving of y-x cents
C. Combined, with a saving of x cents
D. Separately, with a saving of x-y cents
E. Separately, with a saving of y cents

hi there.. could anyone pls help to explain what does it mean by ".......saving of x-y cents, y-x cents" pls?I have difficult understand it..
[Reveal] Spoiler: OA

Last edited by Bunuel on 27 Jan 2012, 06:44, edited 3 times in total.
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Re: To mail a package [#permalink]

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25 Aug 2011, 09:13
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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.
This means it costs x cent for the first pound in weight for example, 20 cents for the first pound.
It costs y cents for the every pound in weight above this, for example 10 cents for pound 2 and 10 cents for pound 3.
x is more than y. for example 20 cents vs. 10 cents

Two packages weighing 3 pounds and 5 pounds, respectively can be mailed seperately or combined as one package. Which method is cheaper and how much money is saved?

Separately cost:
3 pounds: x+2y
5 pounds:x+4y
Total: 2x+6y

Combined cost:
8 pounds: x+7y

So we are saving:
(2X+6y) - x+7y
= x-y cents

Combined is cheaper as we maximise y and minimize x.
1) Combined, with a saving of x-y cents
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Re: To mail a package [#permalink]

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25 Aug 2011, 09:42
miweekend wrote:
nammers wrote:
To mail a package, the rate is x cents for the first pound and y cents for each additional pound, where x>y.
This means it costs x cent for the first pound in weight for example, 20 cents for the first pound.
It costs y cents for the every pound in weight above this, for example 10 cents for pound 2 and 10 cents for pound 3.
x is more than y. for example 20 cents vs. 10 cents

Two packages weighing 3 pounds and 5 pounds, respectively can be mailed seperately or combined as one package. Which method is cheaper and how much money is saved?

Separately cost:
3 pounds: x+2y
5 pounds:x+4y
Total: 2x+6y

Combined cost:
8 pounds: x+7y

So we are saving:
(2X+6y) - x+7y
= x-y cents

Combined is cheaper as we maximise y and minimize x.
1) Combined, with a saving of x-y cents

thank you nammer.

I saw you are using (Separate Cost) - (Combined Cost).
So it is (2x+6y) - (x+7y) = 2x + 6y - x - 7y = x-y <--- it makes sense here to conclude answer is A.

However, if we try using (Combined Cost) - (Separate Cost). isn't it ended up as Answer (B)

(x+7y) - (2x+6y) = x + 7y - 2x - 6y = -x+y which is a y-x

-> Combined, with a saving of y-x cents

I'm stuck here..

(x+7y) - (2x+6y) = x + 7y - 2x - 6y

It is the other way round as we are calculating saving
You save
2x+6y
And spend
x+7y
Therefore you save in total
2x+6y -(x +7y) = x-y
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Re: To mail a package [#permalink]

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25 Aug 2011, 16:30
another way is you can think this as follows

2x+6y vs x+7y

= x+6y+x vs x+6y+y

now we can clearly see x on the LHS and y on the right hand side is the only difference.

also its mentioned in the question that x>y

so the LHS must be greater than RHS. (or RHS < LHS)

In other words x+7y is cheaper than 2x+6y. Find out the difference by subtracting the smaller from the larger.

so combined is cheaper by 2x+6y-(x+7y) = x-y

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Re: To mail a package [#permalink]

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21 Nov 2011, 13:18
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Another way of solving this problem is using numbers in place of x and y
choose $$x = 3$$ and $$y = 2$$ as $$x>y$$

Shipping separately :
3 lb Package: $$3 + 2 *2 = 7$$
5 lb package: $$3 + 4*2 = 11$$
Total cost: 18 lbs

Shipping combined:
Cost = 3 + 7 * 2 = 17 lbs

So shipping combined is cheaper it is cheaper by 1cent(i.e 3-2 or x-y)

Looking at the answer choices - A
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Re: To mail a package [#permalink]

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30 Nov 2011, 23:32
I used numbers for all the variables and got the anwer.I did not use algebra.
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Re: To mail a package [#permalink]

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27 Jan 2012, 06:30
Spidy001 wrote:
another way is you can think this as follows

2x+6y vs x+7y

= x+6y+x vs x+6y+y

now we can clearly see x on the LHS and y on the right hand side is the only difference.

also its mentioned in the question that x>y

so the LHS must be greater than RHS. (or RHS < LHS)

In other words x+7y is cheaper than 2x+6y. Find out the difference by subtracting the smaller from the larger.

so combined is cheaper by 2x+6y-(x+7y) = x-y

thank you! Finally I got it now!!
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Re: To mail a package, the rate is x cents for the first pound [#permalink]

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27 Jan 2012, 06:55
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miweekend 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 seperately or combined as one package. Which method is cheaper and how much money is saved?

A. Combined, with a saving of x-y cents
B. Combined, with a saving of y-x cents
C. Combined, with a saving of x cents
D. Separately, with a saving of x-y cents
E. Separately, with a saving of y cents

If we ship two packages separately it'll cost: $$1x+2y$$ 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 $$(x+2y)+(x+4y)=2x+6y$$;

If we ship them together in one 8pound package it'll cost: $$1x+7y$$ (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.

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

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03 Oct 2013, 08:25
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Re: To mail a package, the rate is x cents for the first pound [#permalink]

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16 Jun 2014, 03:29
Easiest way to do it imho is picking numbers for x and y. E.g. pick 2 $for x and 1$ for y. Then you see that

separately: first package : 3 pounds, hence x +y +y +y = 4 $second package: 5 pounds, hence x +y +y +y +y = 6$
totals 10 $combined: 8 pounds: x +y +y +y +y +y +y +y = 9$

Now you see that you save 1 $if you send the package combined. And 1$ equals 2$(x)-1$(y), hence it's A.
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Re: To mail a package, the rate is x cents for the first pound [#permalink]

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25 Jun 2015, 10:26
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Re: To mail a package, the rate is x cents for the first pound [#permalink]

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30 Jul 2016, 16:00
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Re: To mail a package, the rate is x cents for the first pound [#permalink]

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14 May 2017, 09:15
Bunuel wrote:
miweekend 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 seperately or combined as one package. Which method is cheaper and how much money is saved?

A. Combined, with a saving of x-y cents
B. Combined, with a saving of y-x cents
C. Combined, with a saving of x cents
D. Separately, with a saving of x-y cents
E. Separately, with a saving of y cents

If we ship two packages separately it'll cost: $$1x+2y$$ 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 $$(x+2y)+(x+4y)=2x+6y$$;

If we ship them together in one 8pound package it'll cost: $$1x+7y$$ (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.

Hope it helps.

Hi BB - i cannot understand why we subtracted 'Together' from 'Separately' and not 'Separately' from 'Together'. Can you please help
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Re: To mail a package, the rate is x cents for the first pound [#permalink]

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14 May 2017, 09:57
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Bunuel wrote:
miweekend 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 seperately or combined as one package. Which method is cheaper and how much money is saved?

A. Combined, with a saving of x-y cents
B. Combined, with a saving of y-x cents
C. Combined, with a saving of x cents
D. Separately, with a saving of x-y cents
E. Separately, with a saving of y cents

If we ship two packages separately it'll cost: $$1x+2y$$ 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 $$(x+2y)+(x+4y)=2x+6y$$;

If we ship them together in one 8pound package it'll cost: $$1x+7y$$ (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.

Hope it helps.

Hi BB - i cannot understand why we subtracted 'Together' from 'Separately' and not 'Separately' from 'Together'. Can you please help

First of all, I'm not bb. bb is completely different person. I'm Bunuel.

Next, the question asks which method is cheaper?

Shipping separately costs (2x+6y) = (x + x + 6y) and shipping together costs (x+7y) = (x + y + 6y). Since we are told that x>y, then (x + x + 6y) > (x + y + 6y), thus shipping together is cheaper and this way we are saving (2x+6y) -(x+7y)=x-y.

Hope it's clear.

P.S. This is explained in highlighted part of my post above.
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Re: To mail a package, the rate is x cents for the first pound [#permalink]

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18 May 2017, 20:03
miweekend 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 seperately or combined as one package. Which method is cheaper and how much money is saved?

A. Combined, with a saving of x-y cents
B. Combined, with a saving of y-x cents
C. Combined, with a saving of x cents
D. Separately, with a saving of x-y cents
E. Separately, with a saving 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), in which t is the number of pounds of the package. Let’s first determine the cost of mailing the two 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 of mailing the two individual packages separately is:

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

Now let's determine the cost of mailing 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.

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Re: To mail a package, the rate is x cents for the first pound   [#permalink] 18 May 2017, 20:03
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