Algebra Bridge Project
Cell Phone Plans
Name ___________________________________________
Teacher _____________________
Part I: Two Cell Phone Plans
You are in the market for a new cell phone, and you have narrowed your search to two different cell
phone companies -- EZ-Phone and Phones ‘R’ Us. The plan for each company is as follows:
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EZ-Phone: $25 per month and $0.20 per minute (no free minutes; no texting)
Phones ‘R’ Us: $20 per month and $0.25 per minute (no free minutes; no texting)
Question: Which cell phone company is the better choice for you?
1. For each cell phone plan, let x represent the number of minutes you talk on the phone and let
y represent the total amount of your bill (in dollars) at the end of the month. Complete each of the
following tables of values.
EZ-Phone
x
(# of minutes)
y
(amount of bill)
Phones ‘R’ Us
x
(# of minutes)
0
0
20
20
40
40
60
60
80
80
100
100
120
120
140
140
160
160
180
180
200
200
y
(amount of bill)
2. Graph the points from both plans on the same set of axes. Make sure to label each graph.
3. Which shape is created by each cell phone plan?
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4. Write an equation for the functions you graphed for each of the cell phone companies.
EZ-Phone
Phones ‘R’ Us
Equation:
Equation:
5. For the EZ-Phone plan, what is the value of your slope?
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6. For the Phones ‘R’ Us plan, what is the value of your slope?
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7. In your own words, explain how the value of the slope of the line is related to the cost of each cell
phone plan.
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8. For the EZ-Phone plan, what is the value of your y-intercept?
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9. For the Phones ‘R’ Us plan, what is the value of your y-intercept?
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10. In your own words, explain how the value of the y-intercept of the line is related to the cost of each
cell phone plan.
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11. When would the two cell phone plans cost the same? What would that cost be?
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12. How can you use the graph to determine when the two plans will cost the same and what that cost
will be?
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13. Find when the two plans will cost the same amount by using an algebraic solution. What will that
cost be?
14. Which plan would you choose? Why? Use mathematical reasoning in explaining your choice.
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Part IIa: Talk or Text?
Good news! Your parents just said that they would buy you your first cell phone and prepay $25
each month for the plan of your choice. To make the best decision, you’ve found the two plans
below. Compare the cell phone plans and choose the one that’s right for you.
Voice Minutes
Text Messages
Plan A
5 cents/minute
15 cents/message
Plan B
10 cents/minute
5 cents/message
1. If you choose to only send text messages, which plan will allow you to send the most? How many
will you be able to send?
2. If you choose to only talk on the phone, which plan will allow you to talk the longest? How long
will you be able to talk?
3. If you talk for a total of two hours in a month, how many texts will you be able to send under Plan
A? Under Plan B?
Plan A
Plan B
4. Write an equation for each plan to represent the number of text messages (x) and the number of
voice minutes (y) you will be able to use with the $25. You should have a separate equation for each
plan.
Plan A
Plan B
5. Graph both equations on the same set of axes below. Make sure you label each function.
Work Space
6. Where do the graphs of the equations intersect? What does this point represent?
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7. Find when the two plans will cost the same amount. Only an algebraic solution will be accepted.
8. Which plan would you choose? Why? Use mathematical reasoning in explaining your choice.
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Part IIb: Talk or Text?
Suppose you don’t want to spend all $25 this month because you want the money to carry over into
next month.
1. Write an inequality for Plan A to represent the number of text messages (x) and the number of
voice minutes (y) you will be able to use by spending no more than $25.
2. Graph the inequality on the grid provided below.
3. Can you talk for 250 minutes and send 100 text messages without going over your limit?
(a) Justify your answer algebraically.
(b) Justify your answer graphically.
4. Can you talk for 100 minutes and send 100 text messages without going over your limit? Justify your
answer.
(a) Justify your answer algebraically.
(b) Justify your answer graphically.
5. Write an inequality for Plan B to represent the number of text messages (x) and the number of voice
minutes (y) you will be able to use by spending no more than $25.
6. Graph the inequality on the grid provided below.
7. Can you talk for 150 minutes and send 100 text messages without going over your limit?
(a) Justify your answer algebraically.
(b) Justify your answer graphically.
8. Can you talk for 200 minutes and send 150 text messages without going over your limit? Justify your
answer.
(a) Justify your answer algebraically.
(b) Justify your answer graphically.