
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
April 15th, 2014, 02:49 AM  #1 
Senior Member Joined: Sep 2013 From: Earth Posts: 827 Thanks: 36  Progression problem
Two companies, C and D, offer a different salary scale for the same post: Company C:Starting monthly pay = RM500.00 Thereafter, the monthly salary for a particular month is 10% more than the monthly salary for the preceding month Company D:Starting monthly pay = RM300.00 Thereafter, the monthly salary for a particular month is 15% more than the monthly salary for the preceding month (a)Azrin and Aidil start to work for company C and D respectively in the same month. After how many months will Aidil’s monthly salary be more than Azrin’s monthly salary? Use two methods. (b)Which salary scale is the better deal? Justify. 
April 16th, 2014, 07:02 AM  #2  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  Hello, jiasyuen! Quote:
These are geometric sequences. After $\displaystyle n$ months, Azrin's monthly salary is: $\displaystyle \,500(1.10^n)$ dollars. After $\displaystyle n$ months, Aidil's monthly salary is: $\displaystyle \,300(1.15^n)$ dollars. When is Aidil's salary greater than Azrin's? $\displaystyle \quad 300(1.15^n) \;>\; 500(1.10^n) \quad\Rightarrow\quad \frac{1.15^n}{1.10^n} \;>\;\frac{500}{300}$ $\displaystyle \quad \left(\frac{1.15}{1.10}\right)^n \;>\;\frac{5}{3} \quad\Rightarrow\quad \left(\frac{23}{22}\right)^n \;>\;\frac{5}{3} $ Take logs: $\displaystyle \:\ln\left(\frac{23}{22}\right)^n \;>\; \ln\left(\frac{5}{3}\right) \quad\Rightarrow\quad n\ln\left(\frac{23}{22}\right) \;>\;\ln\left(\frac{5}{3}\right)$ $\displaystyle \quad n \;>\;\frac{\ln\left(\frac{5}{3}\right)}{\ln\left( \frac{23}{22}\right)} \;=\;11.491684...$ Aidil's salary will be greater in 12 months. Quote:
If they plan to work for less than one year, $\displaystyle \quad$ Company C has the better deal. Otherwise, Company D's deal is better.  

Tags 
problem, progression 
Search tags for this page 
(a) azrin and aidil start to work for company c and d respectively in the same month. after how many months will aidil’s monthly salary be more than azrin’s monthly salary? use two methods.,salary scheme with geometric sequence
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Geometric progression problem. Help  jiasyuen  Algebra  5  November 27th, 2013 05:47 AM 
Geometric progression problem  jiasyuen  Algebra  2  November 24th, 2013 07:31 AM 
progression problem  anigeo  Algebra  2  January 18th, 2012 11:41 PM 
Progression Problem  Faux  Algebra  9  January 5th, 2012 07:48 AM 
progression  mikeportnoy  Real Analysis  0  December 31st, 1969 04:00 PM 