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Algebraic Translation.

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by Aishwarya1204 » Mon Oct 15, 2012 5:56 am
The cost of sending a package is T cents for the first 1/4th kilogram and T/5 cents for each additional 1/4 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.

The answer is:
[spoiler] 4(p+1)T/5 [/spoiler]

I understood the solution with picking numbers but want to know how to do this with algebra.

The equation I formed was:

T(1/4)+ T/5(4p-1/4)
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by anuprajan5 » Mon Oct 15, 2012 6:17 am
Aishwarya,

This is my method:

for initial 1/4 kg it is T cents and for every additional 1/4 kg it is T/5 cents.

P is a combination of the above in the form 1/4+a*1/4, where a is the number of additional 1/4 kg.

Therefore a = 4p-1


Now for the cost aspect, this will be equal to T + a*T/5. (for the first 1/4 kg - T cents and every a additional 1/4 kg, it is T/5)

Substituting for a, the cost will be T + (4p-1)*T/5

This when simplified will be 4T*(P+1)/5

Regards
Anup
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by Aishwarya1204 » Mon Oct 15, 2012 6:35 am
Wow thats a nice easy solution !
Thanks alot Anup !
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by Brent@GMATPrepNow » Mon Oct 15, 2012 7:13 am
Aishwarya1204 wrote:The cost of sending a package is T cents for the first 1/4th kilogram and T/5 cents for each additional 1/4 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.

The answer is:
[spoiler] 4(p+1)T/5 [/spoiler]
Since the two different rates are given per 1/4 kilogram, it might be useful to use measurements of 1/4 kg. So, each unit of measurement is 1/4 kg.

Since there are 4 units of measurement per kilogram, and since the package weighs P kilogram, we can say that the package weighs 4P units.

Of these 4P units of weight, the first 1 unit is charged at a rate of T cents. So, the total cost for that 1 unit is T cents.

This leaves 4P-1 units remaining to be charged at a rate of T/5 cents per unit. So, the total cost for those 4P-1 units is (T/5)(4P-1) cents.

So, the total cost is T + (T/5)(4P-1) cents.
When we simplify this, we get [spoiler][4T(1+P)]/5[/spoiler]

Cheers,
Brent
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by vishugogo » Thu Feb 07, 2013 11:37 am
Dear Brent

how to solve by taking numbers.....
Brent@GMATPrepNow wrote:
Aishwarya1204 wrote:The cost of sending a package is T cents for the first 1/4th kilogram and T/5 cents for each additional 1/4 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.

The answer is:
[spoiler] 4(p+1)T/5 [/spoiler]
Since the two different rates are given per 1/4 kilogram, it might be useful to use measurements of 1/4 kg. So, each unit of measurement is 1/4 kg.

Since there are 4 units of measurement per kilogram, and since the package weighs P kilogram, we can say that the package weighs 4P units.

Of these 4P units of weight, the first 1 unit is charged at a rate of T cents. So, the total cost for that 1 unit is T cents.

This leaves 4P-1 units remaining to be charged at a rate of T/5 cents per unit. So, the total cost for those 4P-1 units is (T/5)(4P-1) cents.

So, the total cost is T + (T/5)(4P-1) cents.
When we simplify this, we get [spoiler][4T(1+P)]/5[/spoiler]

Cheers,
Brent
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by Brent@GMATPrepNow » Thu Feb 07, 2013 11:49 am
vishugogo wrote:Dear Brent

how to solve by taking numbers.....
It would be better to have all of the answer choices to show how plugging in numbers works, but let's proceed.

Let's say that T=10 (since this makes T/5 easy to work with)
And let's say that P=2
So, based on the given information, if T=10 cents and a package weighs 2kg, then what's the cost?
Well, it's 10 cents for the first 1/4 kg plus (10/5) cents for every 1/4 kg after.
So, it's 10 cents plus (2)(7) cents
This adds to a total of 24 cents.
In other words, when T=10 and P=2, the cost is 24 cents.

At this point, we check each answer choice to see which one yields a cost of 24 cents when T=10 and P=2

Check [4(p+1)T]/5
Plug in T=10 and P=2 to get [4(2+1)10]/5 = 24 bingo!

Cheers,
Brent
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by Lifetron » Fri Feb 08, 2013 1:51 am
T + { (T/5)*([4*P]-1) }
T + (4P-1)*(T/5)
{5T + 4PT - T}/5
(4T + 4TP)/5
Hence,
4T(1+P)/5
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