Buying a Phone!

Which phone should I buy???

Oh no!

I’m buying a phone, but I don’t know which one to choose! There is one plan which costs $300 for the initial phone plus $15 every month. It does not have data, but has 50 free minutes and 50 texts. The other phone is $200 at its initial cost but costs $65 every month. This phone has unlimited calling, texting AND 1.5 GB of data! If I wanted to buy a plan for 6 months but wanted the cheaper one (even if it means less features), which phone would be less costly?

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Let's Calculate!

Phone Plan # 1:


....Month.... ....Total Cost....

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Initial Cost: $300

  • 1 .......|....... $315
  • 2 .......|....... $330
  • 3 .......|....... $345
  • 4 .......|....... $360
  • 5 .......|....... $375
  • 6 .......|....... $390



Equation: y= 15x+300 Let 'y' represent the total cost and 'x' represent the # of months

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Phone Plan # 2:


....Month.... ....Total Cost....

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Initial Cost: $200

  • 1 .......|....... $265
  • 2 .......|....... $330
  • 3 .......|....... $395
  • 4 .......|....... $460
  • 5 .......|....... $525
  • 6 .......|....... $590



Equation: y= 65x+200 Let 'y' represent the total cost and 'x' represent the # of months

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Line of Intersection

y=15x+300 and y=65x+200


To solve for the point of intersection, we need to find the 'x' and 'y' values of the point. Let's start with the 'x' value. First equal the two equations:


15x+300 = 65x+200


Now solve for 'x' to find part of the point of intersection:


300-200 = 65x-15x

100 = 50x

100/50 = x

2 = x


Therefore the value of 'x' at the intersection of these two lines is 2. So at 2 months, the costs of the phone plan will be the same.


To solve for 'y', we can sub the 'x' value into any or both equations:


y = 15x+300

y = 15 (2) + 300

y = 30 + 300

y = 330


Therefore the value of 'y' at the intersection of these two lines is 330. So when both plans reach $330, it will be the same month.


We can conclude, at two months the total cost of both phone plans will be $330.

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But WHICH Phone!?!

When buying a phone without a plan, 'Plan 2' is less expensive. It stays that way for the first month, but when the second month comes around, both plans cost the same. So if you wanted to get a plan for 2 months, both plans would be the same cost and it wouldn't matter which one you would choose. Since I need a phone plan for 6 months, let's keep looking. Suddenly 'Plan 2' get's more expensive than 'Plan 1'. From this data we can see that it is cheaper to get 'Plan 2' for one month, it costs the same to get both plans for 2 months, and AFTER 2 months 'Plan 1' is cheaper than 'Plan 2'. In this case, I need a plan for 6 months so 'Plan 2' will be cheaper!