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 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
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Hello, jiasyuen!

Quote:
 For the same job, two companies offer a different salary scale: Company A: ​Starting monthly pay = \$900.00 ​Monthly increment = \$50.00 ​ Company B:​ Starting monthly pay = \$750.00 ​Monthly increment = \$60.00 (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.

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:
 (b)​Which salary scale is the better deal? Justify.

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.$\displaystyle \;\;{\color{red}{**}}$

$\displaystyle \begin{array}{c|ccccccccc} \hline \text{Month} & 0 & 1 & 2 & 3 & \cdots & 15 & 16 & 17 & \cdots \\ \hline \text{Ali} & 900 & 950 & 1000 & 1050 & \cdots & 1650 & 1700 & 1750 & \cdots \\ \hline \text{Ahmad} & 750 & 810 & 870 & 930 & \cdots & 1650 & 1710 & 1770 & \cdots \\ \hline \end{array}$

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

$\displaystyle {\color{red}{**}}$
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
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Quote:
 Originally Posted by jiasyuen The question stated there have to use three methods to find. Including of ICT. What it means ? How to do ?
Well, Soroban gave you one; seems fair that YOU find two more;
it is YOUR homework, not ours. Do you agree?

 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
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From: Earth

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Quote:
 Originally Posted by soroban Hello, jiasyuen! 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). 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.$\displaystyle \;\;{\color{red}{**}}$ $\displaystyle \begin{array}{c|ccccccccc} \hline \text{Month} & 0 & 1 & 2 & 3 & \cdots & 15 & 16 & 17 & \cdots \\ \hline \text{Ali} & 900 & 950 & 1000 & 1050 & \cdots & 1650 & 1700 & 1750 & \cdots \\ \hline \text{Ahmad} & 750 & 810 & 870 & 930 & \cdots & 1650 & 1710 & 1770 & \cdots \\ \hline \end{array}$ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ $\displaystyle {\color{red}{**}}$ 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.

Not 16 month?

Ali in Company A:
Tn =a+(n-1)d
=900+(n-1)(50)
=900+50n-50
=850+50n

Tn = a+(n-1)d
=750+(n-1)(60)
=750+60n-60
=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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### in january 2014 ali starts to work in company A and ahmad company b when will the monthly salary of ali and ahmad be the same

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