Rate Problem 4

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phoenix9801: Master | Next Rank: 500 Posts; Posts: 190; Joined: Thu Jan 14, 2010 8:29 pm; Thanked: 2 times

by phoenix9801 » Thu May 31, 2012 4:31 pm

Hi, If someone help me on rate problem please I would greatly Appropriate it. I just want to ensure I have done them correctly. Thanks

Jack made his first x dollars at an average rate of 50 dollars per hour and the remaining amount at an average rate of 60 dollars per hour. How long did it take Jack to make the first x dollars if he worked for a total of 10 hours averaging 53 dollars per hour?

A) 4.5
B) 6
C) 7
D) 9
E) 9.25

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Source: Beat The GMAT — Problem Solving | Thu May 31, 2012 4:31 pm

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu May 31, 2012 5:08 pm

phoenix9801 wrote:Hi, If someone help me on rate problem please I would greatly Appropriate it. I just want to ensure I have done them correctly. Thanks

Jack made his first x dollars at an average rate of 50 dollars per hour and the remaining amount at an average rate of 60 dollars per hour. How long did it take Jack to make the first x dollars if he worked for a total of 10 hours averaging 53 dollars per hour?

A) 4.5
B) 6
C) 7
D) 9
E) 9.25

Total amount earned = 10*53 = 530.

We can plug in the answers, which represent the time worked at a rate of 50 dollars per hour.

Answer choice C: 7 hours at 50 dollars per hour, implying 3 hours at 60 dollars per hour
Total earned = 7*50 + 3*60 = 350+180 = 530.
Success!

The correct answer is C.

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GMAT Kolaveri: Master | Next Rank: 500 Posts; Posts: 287; Joined: Fri Mar 23, 2012 12:33 amFollowed by: 6 members; Location: Pune,India; Thanked: 60 times

by GMAT Kolaveri » Thu May 31, 2012 6:33 pm

Solving using Alligations method: It takes only few seconds to solve
A1------------------------------- A2
50------------------------------60

--------------- Aw
---------------- 53

A2-Aw -------------------------- Aw-A1
60-53--------------------------- 53-50
7------------------------ 3

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eagleeye: Legendary Member; Posts: 520; Joined: Sat Apr 28, 2012 9:12 pmFollowed by: 49 members; Thanked: 339 times; GMAT Score:770

by eagleeye » Thu May 31, 2012 6:55 pm

Here's a traditional math reply. Its a simple equation to solve.

let the time required to make first x dollars be t (when the earning was 50$/hr) and then the remaining time is (10-t) (working at 60$ per hour).

Then we have 50*t + 60* (10-t) = 53*10 => 50t+600-60t=530, hence 10t = 70 or t = 7 hours.

Let me know if this helps

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