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# The cost of sending a package is T cents for the first .25

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Manager
Joined: 14 Dec 2004
Posts: 119
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The cost of sending a package is T cents for the first .25 [#permalink]  14 Dec 2004, 21:01
The cost of sending a package is T cents for the first .25 kilogram
and .2T cents for each additional .25 kilogram or fraction thereof. What is the cost, in cents, to send a P kilogram package at this rate, where P is an integer greater than 1?

1 PT/20
2 (PT-1)/20
3 (.25P+1)T
4 (16PT-T)/20
5 .2(4)(T)(P+1)

I have solved this by plugging in numbers, can someone tell me how to do it with algebra alone? I am curious, it may not be the best way though.
Senior Manager
Joined: 19 May 2004
Posts: 291
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E.
Plugging in can really save time here if you pick numbers.

With Algebra:

I had to start over 5 times before i got it right!
It was quite confusing.

For the first 1/4 Kg: T Cents.
For the next 3: 3*0.2T Cents = 0.6 Cents.
(3 * 1/4 Kg to complete a whole 1Kg.)
We know that the first 1Kg, will cost 1.6T Cents.
What's left is (P-1) Kg. Which contains 4*(p-1) quarters of a Kg.

So the answer is : 1.6T + (P-1)*4*0.2T
Work with that and you get the same equation as in E.
Director
Joined: 21 Sep 2004
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E surely. plugging numbers (thank God for that!!!!!!!)
CIO
Joined: 09 Mar 2003
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Dookie wrote:
E.
Plugging in can really save time here if you pick numbers.

With Algebra:

I had to start over 5 times before i got it right!
It was quite confusing.

For the first 1/4 Kg: T Cents.
For the next 3: 3*0.2T Cents = 0.6 Cents.
(3 * 1/4 Kg to complete a whole 1Kg.)
We know that the first 1Kg, will cost 1.6T Cents.
What's left is (P-1) Kg. Which contains 4*(p-1) quarters of a Kg.

So the answer is : 1.6T + (P-1)*4*0.2T
Work with that and you get the same equation as in E.

yeah, algebraically there are so many ways to work this out, and you might not get the same answer as one of the choices. Dookie's way works great - the way I did it was also right but did not produce any of the answers. I think plugging in worked just fine here.

But what threw me off was the phrase "Or any fraction thereof". Because of that, I assumed this didn't have to be whole number kg's, because a whole number would always have an exact amount of .25kgs. I spent a while trying to figure that out before I realized it said that P was an integer. That was a little weird....
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