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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Algebraic Translation.
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Aishwarya1204
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anuprajan5
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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
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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Aishwarya1204
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Brent@GMATPrepNow
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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.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 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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vishugogo
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Dear Brent
how to solve by taking numbers.....
how to solve by taking numbers.....
Brent@GMATPrepNow wrote: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.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 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
GMAT/MBA Expert
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Brent@GMATPrepNow
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It would be better to have all of the answer choices to show how plugging in numbers works, but let's proceed.vishugogo wrote:Dear Brent
how to solve by taking numbers.....
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
Brent Hanneson - Creator of GMATPrepNow.com
