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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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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..

Originally posted by miweekend on 25 Aug 2011, 09:02.
Last edited by Bunuel on 27 Jan 2012, 06:44, edited 3 times in total.
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Re: To mail a package, the rate is x cents for the first pound  [#permalink]

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New post 27 Jan 2012, 06:55
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3
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.

Answer: A.

Hope it helps.
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Re: To mail a package  [#permalink]

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New post 25 Aug 2011, 09:13
2
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.
Answer is:
1) Combined, with a saving of x-y cents
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Re: To mail a package  [#permalink]

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New post 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.
Answer is:
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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New post 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

Answer is 1.
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Re: To mail a package  [#permalink]

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New post 21 Nov 2011, 13:18
2
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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New post 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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New post 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

Answer is 1.


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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New post 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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New post 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.

Answer: A.

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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New post 14 May 2017, 09:57
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Adityam wrote:
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.

Answer: A.

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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New post 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.

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

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New post 21 Sep 2017, 03:16
Adityam wrote:
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.

Answer: A.

Hope it helps.


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



Please correct the answer if you find an error.

It does not matter if we subtract separately from together or together from separately.

Let x=3 and y= 2 (x>y)

Separately -together= 1 (this shows that S>T and we will have a saving of 1 )

Together- Separately= -1 (this still shows that S>T and we will have a saving of 1 if we go with the together option and a loss of 1 if we go with the other option).


Therefore as the question is asking which method is cheaper and how much money is saved, we will write x-y= 3-2=1 (positive value) as saving cannot be negative.

If the question asked which method is costlier and what's the loss, then we know the answer and the loss would be 2-3= -1 (negative value as its a loss).
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Re: To mail a package, the rate is x cents for the first pound  [#permalink]

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New post 01 Mar 2018, 13:34
Hi All,

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...

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

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New post 23 Mar 2018, 04:59
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

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..


Guys ,
what is the difference between answers A and C ? I chose C

I did following

let x be 2 and y be 1

separately

3 pound package 2 +2 = 4
5 pound package 2 +4 = 6

total 10

combined 3 and 5 pound packages

2 +6 = 8

now 10-8 = 2
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Re: To mail a package, the rate is x cents for the first pound  [#permalink]

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New post 23 Mar 2018, 05:04
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dave13 wrote:
Guys ,
what is the difference between answers A and C ? I chose C

I did following

let x be 2 and y be 1

separately

3 pound package 2 +2 = 4
5 pound package 2 +4 = 6

total 10

combined 3 and 5 pound packages

2 +6 = 8

now 10-8 = 2


Hey dave13 ,

The highlighted text is wrong.

When you combine both, total weight = 8 pounds.

So, cost will be 2 for the 1st and 7 for the rest = 9

Thus difference between the two = 10-9=1

This is equal to x - y. Hence , A is the answer.

Does that make sense?
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Re: To mail a package, the rate is x cents for the first pound  [#permalink]

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New post 23 Mar 2018, 05:55
1
dave13 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

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..


Guys ,
what is the difference between answers A and C ? I chose C

I did following

let x be 2 and y be 1

separately

3 pound package 2 +2 = 4
5 pound package 2 +4 = 6

total 10

combined 3 and 5 pound packages

2 +6 = 8

now 10-8 = 2


Hello dave13,

I will give both the precise and the "start with easy number" approach here.

Approach #1 - Precise:

separate : (1) 3 pound package -> 1 + 2 pounds = x + 2y cents
(2) 5 pound package -> 1 + 4 pounds = x + 4y cents

total = ( x + 2y ) + ( x + 4y ) = 2x + 6y cents

combined : It will be one ( 3 + 5) = 8 pound package.

so ( 1 + 7 pound ) = x + 7y cents

The difference between the two is: combined - separate = ( x + 7y) - (2x + 6y) = y - x

since we know x > y .... y - x will be negative.

hence sending in combined is cheaper and it is cheaper by x - y cents ( negative of y - x ) Option (A)

Approach #2 - Start-with-easy-numbers: This is usually the faster method and is used by you. :-)

et x be 2 and y be 1

separately

3 pound package 2 +2 = 4
5 pound package 2 +4 = 6

total 10

combined 3 and 5 pound packages

2 +7** = 9

now 10-9 = 1 ... which is x - y ( 2 - 1 = 1)

Hope that explains everything...

Best,
Gladi
Re: To mail a package, the rate is x cents for the first pound &nbs [#permalink] 23 Mar 2018, 05:55
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