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Algebra - why ?

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Algebra - why ?

by bhumika.k.shah » Sat Feb 06, 2010 2:46 am
127. 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

Can i solve this sum by using x = 2 and y = 1 ?

What other way can i solve this sum! ?
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by harsh.champ » Sat Feb 06, 2010 2:51 am
bhumika.k.shah wrote:127. 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

Can i solve this sum by using x = 2 and y = 1 ?

What other way can i solve this sum! ?
As we see that x>y,so D and E are eliminated.
Also, y-x <0 ,hence B ruled out.
From the question,it can be found that switching from separate -->>combined will yield a saving of x-y cents.

The ans will be A.
Last edited by harsh.champ on Sat Feb 06, 2010 2:57 am, edited 1 time in total.
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by bhumika.k.shah » Sat Feb 06, 2010 2:54 am
how?

and what abt a,b and c?
harsh.champ wrote:
bhumika.k.shah wrote:127. 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

Can i solve this sum by using x = 2 and y = 1 ?

What other way can i solve this sum! ?
As we see that x>y,so D and E are eliminated.
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by ajith » Sat Feb 06, 2010 3:22 am
bhumika.k.shah wrote:127. 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

Can i solve this sum by using x = 2 and y = 1 ?

What other way can i solve this sum! ?
Say if we are mailing them separately,
the cost for 3 pounds package = x+2y
the cost for 5 pounds package = x+4y

Total cost = 2x+6y

Now if we are mailing them combined, it would be treated as a 8 pound package
the cost = x+7y

The difference between mailing them separately and combined is
2x+6y -x+7y

= x-y

since x>y this is a +ve amount, hence combined is cheaper by an amount of x-y

A
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by harsh.champ » Sat Feb 06, 2010 4:03 am
bhumika.k.shah wrote:how?

and what abt a,b and c?

What other way can i solve this sum! ?
As we see that x>y,so D and E are eliminated.[/quote][/quote]

______________
As i have illustrated in my post (B) can be ruled out because y-x will be expenditure not savings.

As we see that x>y,so D and E are eliminated.
Also, y-x <0 ,hence B ruled out.
From the question,it can be found that switching from separate -->>combined will yield a saving of x-y cents.
Now,if you are having some problem mapping the question in your mind ,plug-in numbers.
Suppose x=4 cents, y=2 cents.

Now,
(A)Taking combined = 8 pounds.
Hence,total cost incurred= 4(for the 1st pound) + 7x2 = 18cents

(B)Taking separate = 5 + 3
Hence,total cost incurred = [4(for the 1st pound) + 4x2] + [4(for the 1st pound) + 2x2]
= 12 + 8
= 20 cents

So,savings = 20 - 18 = 2 cents i.e. x-y
Can i solve this sum by using x = 2 and y = 1 ?

What other way can i solve this sum! ?
Though I have pointed out the soln. but if you are uncomfortable you can definitely plug in the values and save some time.
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by bhumika.k.shah » Sat Feb 06, 2010 4:51 am
Yea i got the sum by taking x = 5 and y = 1

I just wanna know one thing ,
can i take x = 2 and y = 1 ?
harsh.champ wrote:
bhumika.k.shah wrote:how?

and what abt a,b and c?

What other way can i solve this sum! ?
As we see that x>y,so D and E are eliminated.
[/quote]

______________
As i have illustrated in my post (B) can be ruled out because y-x will be expenditure not savings.

As we see that x>y,so D and E are eliminated.
Also, y-x <0 ,hence B ruled out.
From the question,it can be found that switching from separate -->>combined will yield a saving of x-y cents.
Now,if you are having some problem mapping the question in your mind ,plug-in numbers.
Suppose x=4 cents, y=2 cents.

Now,
(A)Taking combined = 8 pounds.
Hence,total cost incurred= 4(for the 1st pound) + 7x2 = 18cents

(B)Taking separate = 5 + 3
Hence,total cost incurred = [4(for the 1st pound) + 4x2] + [4(for the 1st pound) + 2x2]
= 12 + 8
= 20 cents

So,savings = 20 - 18 = 2 cents i.e. x-y
Can i solve this sum by using x = 2 and y = 1 ?

What other way can i solve this sum! ?
Though I have pointed out the soln. but if you are uncomfortable you can definitely plug in the values and save some time.[/quote]
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by ajith » Sat Feb 06, 2010 5:01 am
bhumika.k.shah wrote:Yea i got the sum by taking x = 5 and y = 1

I just wanna know one thing ,
can i take x = 2 and y = 1 ?
You can take any value as long as x is greater than y
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by harsh.champ » Sat Feb 06, 2010 5:32 am
bhumika.k.shah wrote:Yea i got the sum by taking x = 5 and y = 1

I just wanna know one thing ,
can i take x = 2 and y = 1 ?


______________
As i have illustrated in my post (B) can be ruled out because y-x will be expenditure not savings.

As we see that x>y,so D and E are eliminated.
Also, y-x <0 ,hence B ruled out.
From the question,it can be found that switching from separate -->>combined will yield a saving of x-y cents.
Now,if you are having some problem mapping the question in your mind ,plug-in numbers.
Suppose x=4 cents, y=2 cents.

Now,
(A)Taking combined = 8 pounds.
Hence,total cost incurred= 4(for the 1st pound) + 7x2 = 18cents

(B)Taking separate = 5 + 3
Hence,total cost incurred = [4(for the 1st pound) + 4x2] + [4(for the 1st pound) + 2x2]
= 12 + 8
= 20 cents

So,savings = 20 - 18 = 2 cents i.e. x-y
Can i solve this sum by using x = 2 and y = 1 ?

What other way can i solve this sum! ?
Though I have pointed out the soln. but if you are uncomfortable you can definitely plug in the values and save some time.
[/quote]

Though pointed out by ajith that you can take any values as long as x>y.
But still I would recommend that you take dissimilar values such as 5,3 or 7,5.
The reason being:-Suppose you take the value as 2 and 1.
In the end ,you get the savings as 1.Now, that can be y also and x-y also (you took x=2 and y=1).
So again you have to look as to how you solved the question and thus end up spending more time.

Now, suppose you took 5 and 3.
Savings=2 so you can easily see that it is x-y.[not x ,not y , not y-x ]

Hope,you keep it in mind.
While plugging also we have to intelligently pick the values.
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by Jeff@TargetTestPrep » Thu Dec 14, 2017 9:51 am
bhumika.k.shah 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

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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