Phone Bill Plans

A Linear System By Misha Saini

Situation Statement:

Allison is in Canada for Christmas break for 2 weeks. Allison is trying to decide which phone company plan to chose to be able to call back home in Brazil. Allison is in search of a plan that is inexpensive if she calls back home 2 times a week for 25 minutes each time. She has the option to chose from either TELUS Mobile or Virgin Mobile. TELUS has a special promotion going on where they charge the customer $0.50 per minute, whereas Virgin is charging $0.10 per minute will additional fixed charge of $26.

Solving the Situation

By using a table Allison can decipher whether TELUS's plan or Virgin's plan is inexpensive. In the plans below, the variable C is classified as the cost, in dollars, whereas the variable m represents the amount of minutes.
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Graphic Solution:

The graph displayed below shows these two plans plotted.
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The Intersection:

As seen above in the graph, both plans intersect at coordinates 65, 32.5. Both lines will cross at 65 minutes with cost of $32.50. Below is the graphic equation:


To do so, Allison should first substitute the cost of TELUS's plan (0.50m) into Virgins plan (0.10m + 26).

0.50m = 0.10m + 26

0.50m - 0.10m = 26

0.40m = 26

Allision must divide both sides by 0.40.

0.40m/0.40 = 26/0.40

m= 65

Therefore, both these plans do intersect at 65 minutes, now Allison must substitute 65 as m.

TELUS plan: C= 0.50(65)

C= 32.50

Virgin plan: C= 0.10(65) + 26

C= 32.50

Solution:

Therefore, after looking at the tables, graphs and equations displayed above, we can come to the conclusion that Virgins plan is the cheapest plan available for Allison. We know this because when inputted minutes into the table, the output result differs greatly in price from TELUS's output. We can observe that TELUS offers a great plan for someone who wants to call for less than 65 minutes. However, Allison wants to call home 2 times each week for 2 week for about 25 minutes. As shown in the tables Virgin has a cheaper price of $36 for 100 minutes whereas TELUS's price is $50 for 100 minutes which is higher than Virgin's price by $14.

Situation Conclusion:

Allison knows that despite TELUS having a special promotion, Virigin's regular deal price of plan is the best option for her to save money.