Certificate II General Education: Linear Equations and Problem Solving

This assignment focuses on solving real-world linear equations, using a cell phone billing scenario to illustrate the concepts. The student is tasked with comparing two companies' monthly billing policies, writing expressions, creating tables of values, and drawing graphs to analyze the costs. The assignment requires the student to determine the point where the monthly costs are equal, both graphically and algebraically. Further, it explores which plan offers more minutes for a given budget and which plan is more expensive for a specific usage. The student concludes by providing a statement on which plan is best for different usage situations. The solution demonstrates the application of algebraic principles to practical problems, referencing supporting materials.

VU21365 – INVESTIGATE AND USE SIMPLE MATHEMATICAL FORMULAE AND
PROBLEM SOLVING TECHIQUES IN A RANGE OF CONTEX
Student Name ____________________________ Student ID
________________
Student Signature _________________________ Date ___________________
Solving Real World Linear Equations
Jonas needs a cell phone. He has a choice between two companies with the
following monthly billing policies. Each company’s monthly billing policy has an initial
operating fee/flat rate and charge per minute.
Flat rate ($) Charge/minute ($)
Starphone network 29.95 0.14
Telecomms Plus 4.95 0.39
1. Write an expression for the monthly bill for each company using the
variables below 1.
y=total monthly bill
x=number of minutes spoken
Starphone network
y=0.14 x+29.95
Telecomms plus
y=0.39 x +4.95
2. Draw up a table of values for each company
Starphone network
1Barnett, R.A.; Ziegler, M.R.; Byleen, K.E. (2008), College Mathematics for Business,
Economics, Life Sciences and the Social Sciences (11th ed.), Upper Saddle River, N.J.:
Pearson
22237VIC – Certificate II General Education for Adults
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VU21365 – INVESTIGATE AND USE SIMPLE MATHEMATICAL FORMULAE AND
PROBLEM SOLVING TECHIQUES IN A RANGE OF CONTEX
x (minutes) 0 10 20 30 60
y (total
monthly bill
29.95 31.35 32.75 34.15 38.35
Telecomms Plus
x (minutes) 0 10 20 30 60
y (total
monthly bill
4.95 8.85 12.75 16.65 28.35
3. Draw a graph of information. At how many minutes is the monthly cost
the same? (hint: look at the point where the lines intersect. What do the
x∧ y values represent?)
The monthly cost of the communication is similar between the two
companies at the 100th minute.
The x values represent the minutes spoken while the y values indicate
the total monthly bill payable for every minute spoken 2.
2 Jacobson, Nathan (2009), Basic Algebra 1 (2nd ed.), Dover
22237VIC – Certificate II General Education for Adults
ADF-Maths

VU21365 – INVESTIGATE AND USE SIMPLE MATHEMATICAL FORMULAE AND
PROBLEM SOLVING TECHIQUES IN A RANGE OF CONTEX
4. What is the equal monthly cost as determined by the graph.
From the above graph. The total monthly bill at the 100th minute is $
43.95. this is the equal monthly cist for the two companies.
5. Use algebra to find the number of minutes where the monthly cost is
the same. (hint: find the value for x when the 2 equations are equal)
For Starphone the equation is
y=0.14 x+29.95
While for Telecomms plus, the equation is
y=0.39 x +4.95
When the values of y are equal for the two companies we have
0.14 x +29.95=0.39 x + 4.95
0.14 x +25=0.39 x
0.25 x=25
x=100minutes
6. Show algebraically for each equation that the monthly cost is the same
for the number or minutes as shown in question 5.
For Starphone network
y=0.14 x+29.95
At x=100
We have
y= ( 0.14∗100 ) +29.95=$ 43.95
On the other hand
For Telecomms plus
y=0.39 x +4.95
At x=100
22237VIC – Certificate II General Education for Adults
ADF-Maths

VU21365 – INVESTIGATE AND USE SIMPLE MATHEMATICAL FORMULAE AND
PROBLEM SOLVING TECHIQUES IN A RANGE OF CONTEX
y= ( 0.39∗100 ) + 4.95=$ 43.95
Since for each case the value of y is obtained as $ 43.95, we have
proved using algebra that the values are the same at the 100th minute.
7. Which plan provides more minutes for $60? You can use either your
graph or algebra to explain the answer.
Using algebra at $ 60, under Starphone we can obtain
y=0.14 x+29.95
60=0.14 x +29.95
x= 60−29.95
0.14 =214.64 minutes
While under Telecomms, we have
y=0.39 x +4.95
60=0.39 x+ 4.95
x= 60−4.95
0.39 =141.15 minutes
This shows that at $ 60, one can obtain more minutes under
Starphone. The Starphone is higher that the Telecomms plus deal by
73.49 minutes.
8. Which plan costs more if you spoke for 150 minutes each month? You
can use either your graph or algebra to explain the answer.
Using algebra, under Starphone speaking for 150 minutes costs;
Starphone network
y=0.14 x+29.95
y= ( 0.14∗150 ) +29.95=$ 50.95
22237VIC – Certificate II General Education for Adults
ADF-Maths

VU21365 – INVESTIGATE AND USE SIMPLE MATHEMATICAL FORMULAE AND
PROBLEM SOLVING TECHIQUES IN A RANGE OF CONTEX
While under Telecomms plus, we have
y=0.39 x +4.95
y= ( 0.39∗150 ) + 4.95=$ 63.45
This shows that when speaking for 150 minutes you will spend more
under the Telecomms plan than when using the Starphone plan.
9. Write a statement explaining which plan would be best in different
types of situations. Refer to the information in your graph or equations.
From the information on the graph, when an individual is to speak for
less than 100 minutes its recommended to use the telecoms Plus
network as it is the cheaper option.
At the 100minuts mark the two options are indifference.
When speaking for more than 100 minutes then its recommended to
switch to Starphone as it becomes cheaper under this scenario.
22237VIC – Certificate II General Education for Adults
ADF-Maths

VU21365 – INVESTIGATE AND USE SIMPLE MATHEMATICAL FORMULAE AND
PROBLEM SOLVING TECHIQUES IN A RANGE OF CONTEX
References
Barnett, R.A.; Ziegler, M.R.; Byleen, K.E. (2008), College Mathematics for Business,
Economics, Life Sciences and the Social Sciences (11th ed.), Upper Saddle River,
N.J.: Pearson
Jacobson, Nathan (2009), Basic Algebra 1 (2nd ed.), Dover
22237VIC – Certificate II General Education for Adults
ADF-Maths