Kaplan Problem Solving

[debmalya_dutta]

The cost of sending a package is T cents for the first 1/4 kg and T/5 cents for each additional 1/4 kg or fraction thereof. what is the cost of sending a P kg package at this rate where P is an integer greater than 1 ?

Express the answer in terms of P and T

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

I got the answer as
[spoiler](16P+1)T/20..but kaplan doesn't say so..[/spoiler]

[diebeatsthegmat]

The cost of sending a package is T cents for the first 1/4 kg and T/5 cents for each additional 1/4 kg or fraction thereof. what is the cost of sending a P kg package at this rate where P is an integer greater than 1 ?

Express the answer in terms of P and T

1/4 kg costs T
so 3/4 kg costs 3/4*T/5=3t/20
thus 1 kg cost totally T+3T/20 =23T/20
the p kg cost P*23T/20
is that the answer

[debmalya_dutta]

The cost of sending a package is T cents for the first 1/4 kg and T/5 cents for each additional 1/4 kg or fraction thereof. what is the cost of sending a P kg package at this rate where P is an integer greater than 1 ?

Express the answer in terms of P and T

1/4 kg costs T
so 3/4 kg costs 3/4*T/5=3t/20
thus 1 kg cost totally T+3T/20 =23T/20
the p kg cost P*23T/20
is that the answer

Let me give you the options..Give me a couple of minutes and I will also add the options to the question

[kvcpk]

The cost of sending a package is T cents for the first 1/4 kg and T/5 cents for each additional 1/4 kg or fraction thereof. what is the cost of sending a P kg package at this rate where P is an integer greater than 1 ?

Express the answer in terms of P and T

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

I got the answer as
[spoiler](16P+1)T/20..but kaplan doesn't say so..[/spoiler]

0.25 - T cents
0.25 * n -> T/5 *n
P>1
cost for 1 kg = T + 3T/5 = 8T/5
for the next 1 KG, it is 4T/5
means for 2 kg cost = 12T/5. When T=5, P =2 -> cost = 12
out of the options, only E satisfies.

However, to do mathematically,
Let the cost be C
P = 0.25 + 0.25 *n
C = T + n*T/5
(C-T)/T * 5 = n

Substitute n in the eqtn for p.

0.25 + (C-T)*5/T * 0.25 = P
4p-1 = 5c/t - 5
4p=5c/t -4
4(p+1) = 5c/t
4(p+1)T/5 = c

Hope this helps!!

[debmalya_dutta]

The cost of sending a package is T cents for the first 1/4 kg and T/5 cents for each additional 1/4 kg or fraction thereof. what is the cost of sending a P kg package at this rate where P is an integer greater than 1 ?

Express the answer in terms of P and T

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

I got the answer as
[spoiler](16P+1)T/20..but kaplan doesn't say so..[/spoiler]

0.25 - T cents
0.25 * n -> T/5 *n
P>1
cost for 1 kg = T + 3T/5 = 8T/5
for the next 1 KG, it is 4T/5
means for 2 kg cost = 12T/5. When T=5, P =2 -> cost = 12
out of the options, only E satisfies.

However, to do mathematically,
Let the cost be C
P = 0.25 + 0.25 *n
C = T + n*T/5
(C-T)/T * 5 = n

Substitute n in the eqtn for p.

0.25 + (C-T)*5/T * 0.25 = P
4p-1 = 5c/t - 5
4p=5c/t -4
4(p+1) = 5c/t
4(p+1)T/5 = c

Hope this helps!!

A question here...
What is wrong with this approach?

cost of first 1/4 kg = T
remaining weight = P-(1/4)
So the cost of the remaining weight = {[P -(1/4) ] / 0. 25 } * T/5
so total cost = T*1/4 + {[P -(1/4) ] / 0. 25 } * T/5

Am I overlooking something ?

[kvcpk]

A question here...
What is wrong with this approach?

cost of first 1/4 kg = T
remaining weight = P-(1/4)
So the cost of the remaining weight = {[P -(1/4) ] / 0. 25 } * T/5
so total cost = T*1/4 + {[P -(1/4) ] / 0. 25 } * T/5

Am I overlooking something ?

Why are you dividing the weight by 0.25. you should be multiplying by 0.25 or dividing by 4
thats ur mistake

[debmalya_dutta]

A question here...
What is wrong with this approach?

cost of first 1/4 kg = T
remaining weight = P-(1/4)
So the cost of the remaining weight = {[P -(1/4) ] / 0. 25 } * T/5
so total cost = T*1/4 + {[P -(1/4) ] / 0. 25 } * T/5

Am I overlooking something ?

Why are you dividing the weight by 0.25. you should be multiplying by 0.25 or dividing by 4
thats ur mistake [/quote

Did you mean in this equation - {[P -(1/4) ] / 0. 25 } * T/5 ?

P -(1/4) = remaining kgs
0.25 kg costs T/5
then (P-0.25) kgs cost (P-0.25)/0.25 * T/5 cents

I'am probably being slow here..What's wrong with the eqn?

[kvcpk]

Did you mean in this equation - {[P -(1/4) ] / 0. 25 } * T/5 ?

P -(1/4) = remaining kgs
0.25 kg costs T/5
then (P-0.25) kgs cost (P-0.25)/0.25 * T/5 cents

I'am probably being slow here..What's wrong with the eqn?

I am sorry.. actually u were right.. only ur calculation for T was wrong.
Final eqtn for cost u got was:
T/4 + {[P -(1/4) ] / 0. 25 } * T/5

It is not T/4 actually. it is only T.
for first 1/4 kg, cost is T not T/4

so final eqtn should be:
T + {[P -(1/4) ] / 0. 25 } * T/5
solve this and u will reach E

Hope this helps!!