# 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?

## Let's Calculate!

**Phone Plan # 1**:

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

______________________________

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

**____________________________________________________________________________________________________**

**Phone Plan # 2:**

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

_______________________________

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

## Line of Intersection

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.