BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Target Test Prep · GMAT

Choose how you want to prepare

Learn live with an expert or move at your own pace. Every option includes the complete TTP study system.

★★★★★5.0559 reviews
GMATLiveTeach 7 seats left
Chris Peckover
NEXT LIVE COHORT

Oct 13 to Jan 7, 2027

with Chris Peckover

Schedule
Tue, Thu · 8:00 to 10:00 PM ET
Included
40 live hours + 6 months of GMAT OnDemand
  • Live instruction and real-time questions
  • Class recordings and assigned practice
View class & enroll
Limited cohort · enrollment openTarget Test Prep
EALiveTeach 5 seats left
Logan Thompson
EXECUTIVE ASSESSMENT

Sep 6 to Dec 6, 2026

with Logan Thompson

Schedule
Sun · 9:30 AM to 12:30 PM ET
Included
40 hours of live online classes plus six months of access to the complete TTP EA OnDemand course.
  • 165+ EA Score Guarantee
  • 4,100+ Quant, Verbal, and Integrated Reasoning practice questions
  • 400+ hours of in-depth video lessons
  • 3,000+ step-by-step video solutions
View EA class & enroll
Limited cohort · enrollment openTarget Test Prep
GMATOnDemand Start anytime
SELF-PACED MASTERCLASS

Target Test Prep GMAT OnDemand

Complete access from day one. Study on your schedule.

715+ score guarantee
$0to start then $127/mo
  • Personalized study plan and analytics
  • Thousands of lessons and practice questions
Start free 5-day trial
Read 559 reviewsTarget Test Prep

Compare the format, schedule, and included access before enrolling. Prices and seat counts shown reflect the supplied offer details.

Algebraic Translation.

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 18
Joined: Sun Oct 14, 2012 1:08 am
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)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
User avatar
Master | Next Rank: 500 Posts
Posts: 279
Joined: Mon Jun 25, 2012 10:56 pmFollowed by: 10 members
Thanked: 60 times

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
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Junior | Next Rank: 30 Posts
Posts: 18
Joined: Sun Oct 14, 2012 1:08 am

by Aishwarya1204 » Mon Oct 15, 2012 6:35 am
Wow thats a nice easy solution !
Thanks alot Anup !
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770

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
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 131
Joined: Tue Aug 30, 2011 4:50 amFollowed by: 6 members
Location: India
Thanked: 28 times

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
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770

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
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 308
Joined: Thu Mar 29, 2012 12:51 amFollowed by: 3 members
Thanked: 16 times

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
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1