April 15th, 2014, 02:49 AM  #1 
Senior Member Joined: Sep 2013 From: Earth Posts: 827 Thanks: 36  Progression .
For the same job specifications, two companies offer a different salary scale: Company A :Starting monthly pay = RM900.00 Monthly increment = RM50.00 Company B:Starting monthly pay = RM750.00 Monthly increment = RM60.00 (a)In January 2014, Ali starts to work in Company A and Ahmad in Company B. When will the monthly salary of Ali and Ahmad be the same? Use three methods. Include the use of ICT. (b)Which salary scale is the better deal? Justify. How to solve this problem ? Especially problem b. 
April 15th, 2014, 10:20 PM  #2  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  Hello, jiasyuen! Quote:
You need to construct algebraic expressions for Ali's and Ahmad's monthly pay. Ali starts at \$900 per month and gets a \$50 raise each month. When he has worked for $\displaystyle m$ months, $\displaystyle \quad$his monthly pay will be: $\displaystyle \:900 + 50m$ dollars. Ahmad starts at \$750 per month and gets a \$60 raise each month. When he has worked for $\displaystyle m$ months, $\displaystyle \quad$his monthly pay will be $\displaystyle \,750 +60m$ dollars. When are these equal? $\displaystyle \quad 750 + 60m \:=\:900 + 50m \quad\Rightarrow\quad 10m \:=\:150 \quad\Rightarrow\quad m \,=\,15$ Their salaries will be equal in 15 months (March 2015). Quote:
If Ali considers this a temporary job (less than 15 months), $\displaystyle \quad$ he has the better deal. If both are planning to work more than 15 months, $\displaystyle \quad$ then Ahmad has the better deal.$\displaystyle \;\;{\color{red}{**}}$ $\displaystyle \begin{array}{cccccccccc} \hline \text{Month} & 0 & 1 & 2 & 3 & \cdots & 15 & 16 & 17 & \cdots \\ \hline \text{Ali} & 900 & 950 & 1000 & 1050 & \cdots & 1650 & 1700 & 1750 & \cdots \\ \hline \text{Ahmad} & 750 & 810 & 870 & 930 & \cdots & 1650 & 1710 & 1770 & \cdots \\ \hline \end{array}$ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ $\displaystyle {\color{red}{**}}$ I gave this problem some extra thought . . . In 15 months their monthly pay is the same. But Ali has made \$18,750 while Ahmad has made only \$17,550. It will take 31 months for Ahmad's total earnings to equal that of Ali. After that, Ahmad's total earnings will exceed Ali's.  
April 16th, 2014, 03:43 AM  #3 
Senior Member Joined: Sep 2013 From: Earth Posts: 827 Thanks: 36 
The question stated there have to use three methods to find. Including of ICT. What it means ? How to do ?

April 16th, 2014, 09:08 AM  #4 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  
April 16th, 2014, 09:12 AM  #5 
Senior Member Joined: Sep 2013 From: Earth Posts: 827 Thanks: 36 
I don't know what's another two methods ? Can you give me some guidance ?

April 23rd, 2014, 04:36 AM  #6  
Senior Member Joined: Sep 2013 From: Earth Posts: 827 Thanks: 36  Quote:
Not 16 month? Ali in Company A: Tn =a+(n1)d =900+(n1)(50) =900+50n50 =850+50n Ahmad in Company B: Tn = a+(n1)d =750+(n1)(60) =750+60n60 =690+60n When the monthly salary of Ali and Ahmad the same, 850+50n=690+60n 160n=10n n=16 (i.e. in the 16th month)  

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