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Submitted By BAJEEP
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Mike Henkle

Western Governors University

A. Create a story problem using one of the above real-world scenarios as a basis, including realistic numeric values, by doing the following: 1. Describe the real-world problem.

I was looking into phone plans and stumbled upon T-Mobile, and I decided that I needed a cell-phone and took a look at the plans. T-mobile had one plan that was 50 dollars a month and is unlimited talk, text and web, T-Mobile also has a plan for 30 dollars a month for 1,500 talk and text minutes. After you go through your allotted 1,500 talk and text time was up, the cost skyrockets up to 10 cents a minute. 10 cents a minute comes out to 6.00 per hour, I thought in my head. I decided that instead of jumping into a decision about phone plans, that I should first go home and do the math. I wanted to figure out which plan was going to be the most cost effective, and which plan would suite my needs the best.

2. Explain all needs (e.g., financial, non-financial, situational) of the hypothetical consumer.
The needs include many different factors: • The first and most important factor how much do you use your phone? The breaking point on the problem today is 200 talk or text above the 1500 minute plan and I will be paying less up front but more on the back end which is no good. If I chose the 1500 minute plan, I will not want to be going over the 1500 minutes as then the cost would go up to 10 cents a minute or 6.00 per hour. • Is this replacing a work or office phone? If I am going to use this phone for several purposes it is more valuable to me and it is easier to justify higher costs. • What should I do right now if I am unsure but need a phone? I would say the best starting point unless I use my phone all the time is to try out the 30 dollar a month plan. Saving 20 dollars right off the bat and then closely monitoring your minutes over the next couple of months to see which plan benefits you the most is the most logical approach that I can think of.

2. Discuss two cost options that are being considered.

A. Unlimited plan 50 dollars a month

B. 1500 talk and text minutes 30 a month but 10 cents a minute after the 1500.

B. Analyze the cost of each option algebraically by doing the following:

Algebraic Expression
50=30+.10x

• The 50 in the problem comes from the cost of the unlimited plan, this is important because the whole idea behind the expression is to find the break-even point. Once I establish my break-even point, then it is time to figure out other factors that way into the equation. For instance will I use my phone enough to go over the 1500 talk and text plan. I also want to point out that because the 50 will never change due to minutes it’s all by itself on the one side of the equation. • The 30 in the problem comes from the 30 dollars a month to have the 1500 talk and text plan. • .10x is for the 10 cents a minute it will cost when I go over my talk and text plan.

3. Solve the system of equations algebraically to determine where the two cost options are Equivalent.

50=30+.10x
-30 from both sides
20=.10x
Divide both sides by .10
200=x

If I go with the 30 dollar a month plan, with the 1500 minutes and I go over by more than 200 minutes it will cost me more than if I was with the unlimited plan.

a. Explain each step used to solve the system of equations. Include the following in your explanation:
• All mathematical operations used to solve the system of equations
50=30+.10x
-30 from both sides
20=.10x
Divide both sides by .10
200=x

If I go with the 30 dollar a month plan, with the 1500 minutes and I go over by more than 200 minutes it will cost me more than if I was with the unlimited plan.

• The solution(s) of the system of equations in ordered-pair notation
Y=(0,50)(0,30)

60

45

30

15

50 100 150 200 250

• Y-axis= the cost per month for each phone plan • X-axis= the number of minutes • The entire problem takes place in quadrant 1 • The red line the unlimited plan, you will notice that the red line stays consistent; this is simply because it is an unlimited plan and therefore is not affected by number of minutes. • The blue line is the 30 dollars a month plan, with 1500 talk and text minutes, and the amount it will cost if I go over the 1500 minutes. This graph also illustrates the break-even point of 200 additional talk and text minutes for the 30 plan • (200,50) is the point where they break-even.

D.
• How financial information gleaned from your algebraic and graphical analyses can be used to determine the conditions for choosing cost option A over cost option B and vice versa

• The biggest determining factor is trying to figure out if I will even use the 1500 minutes, because if I won’t use more than the 1500 minutes it would be cost effective to go with the plan that is 20 dollars cheaper right out of the gate. • On the other hand, if I am going to be using my phone all the time and will easily go over the 1500 minutes, then I should start right away with the unlimited plan. • Other factors include, am I using this phone as a business phone and personal phone or only a personal phone. If I can rationalize that part of the phone cost is business related, its make the phone more valuable.
• How non-financial, or situational, considerations can impact the decision-making process • This comes back to the minutes, as will I need more than the 1500 minutes, or will the 1500 minutes alone be enough to get me by.

1. Discuss a final recommendation that states the option that most closely meets the
Consumer’s financial needs and non-financial considerations. • Without knowing the exact amount that I will be using my phone, I have decided to go with the 30 dollars a month plan for the first month, and I will continue to check minutes. I will than evaluate, by the number of minutes and text’s that I am going through which option will be best. I will have to monitor and treat this as an ongoing experiment for the next 3 months or so to develop a proper sample of data.

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