My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
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.
jiasyuen is offline  
 
April 15th, 2014, 10:20 PM   #2
Math Team
 
Joined: Dec 2006
From: Lexington, MA

Posts: 3,267
Thanks: 408

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.

soroban is offline  
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 ?
jiasyuen is offline  
April 16th, 2014, 09:08 AM   #4
Math Team
 
Joined: Oct 2011
From: Ottawa Ontario, Canada

Posts: 14,597
Thanks: 1038

Quote:
Originally Posted by jiasyuen View Post
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?
Denis is offline  
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 ?
jiasyuen is offline  
April 23rd, 2014, 04:36 AM   #6
Senior Member
 
Joined: Sep 2013
From: Earth

Posts: 827
Thanks: 36

Quote:
Originally Posted by soroban View Post
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

Ahmad in Company B:
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)
jiasyuen is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
progression



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
progression problem anigeo Algebra 2 January 18th, 2012 11:41 PM
Progression Problem Faux Algebra 9 January 5th, 2012 07:48 AM
progression panky Algebra 1 December 8th, 2011 09:32 AM
progression mikeportnoy Algebra 3 October 14th, 2008 01:42 AM
progression mikeportnoy Real Analysis 0 December 31st, 1969 04:00 PM





Copyright © 2019 My Math Forum. All rights reserved.