Choosing a Cell Phone Plan-Verizon
Investigating Linear Equations
n 2008, Verizon offered the following cell phone plans to consumers. (Source: www.verizon.com)
Verizon: Nationwide Basic
Monthly Anytime Minutes Monthly Fee Charge for Extra Minutes
450 minutes $39.99 $0.45 per minute
900 minutes $59.99 $0.40 per minute
1350 minutes
$79.99
$0.30 per minute
1. If a customer expects to use 500 minutes per month, which plan is the best value?
450 Plan: $39.99 + (50 extra minutes)($0.45 per minute) = $62.49
900 Plan: $59.99
For this customer, the 900 minute plan costs less that the 450 minute plan.
2. A cell phone plan consists of a fixed cost (the monthly fee) and a variable cost (charge for extra
minutes). Find a linear function that gives the total cost of each plan when
x
extra minutes are used.
( )
( )
= +
= +
= +
()
()
Total Cost F i xed Cost V ari able Cost
Monthly Fee Cost per Extra Minute Extra Minute
Monthly Fee Cost per Extra Minute x
450 Plan:
= +39.99 0.45Cx
900 Plan:
= +59.99 0.40Cx
1350 Plan:
= +79.99 0.30Cx
3. Using the cost functions from (2) above, determine the cost of using 600 total minutes and 1000 total
minutes with each plan. Then determine which plan is the best deal for each level.
For the 450 Plan, 600 minutes requires 150 minutes more than the included minutes and 1000
mi nutes requi r es 55 0 mi nutes more than the included minutes. For the 900 Plan, 0 and 100 extra
mi nutes ar e needed, r especti vely. F or the 13 50 Pl an, no extra mi nutes are needed.
Plan 600 minutes 1000 minutes
450
39.99 0.45(150) $107.49
=+=39.99 0.45(550) $287.49C
900
=+=
59.99 0.40(0) $59.99C
*
=+=59.99 0.40(100) $99.99C
1350
=+=
79.99 0.30(0) $79.99C
=+=
39.99 0.30(0) $79.99C
*
I
4. The number of minutes a person uses each month often varies. Suppose that a Verizon customer uses
the total number of minutes shown below.
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
423 441 404 387 417 628 448 402 356 402 436 639
Which plan would cost the consumer the least amount money over the year?
Thi s consumer used less than 45 0 mi nutes a month ever y month except J une and December. In June,
they used 178 extra minutes and in December they used 189 extra minutes. In total, they used 367
extra minutes throughout the year. The basic fee for the 450 Plan is $39.99 per month so their annual
cost i s
( )
( )
( ) ( )
( ) ( ) ( ) ( )
= +
= +
= +
=
39.99 12 0.45 367
479.88 165.15
645.03
Annual Cost Monthly fee months cost per minute extra minutes
The annual cost for the 450 Plan is $645.03.
The 90 0 Plan costs $59. 99 per month for all 12 months for a total cost of $71 9. 8 8. E ven though the
consumer had to pay extr a duri ng June and December, the 45 0 Pl an was sti ll less expensi ve than the
900 Plan.
5.
At what number of extra minutes does the annual cost of the 900 Plan become less expensive than the
450 Plan?
The annual cost of the 450 Plan if no extra minutes are used is
( ) ( )
=39.99 12 $479.88
. Extra minutes
are $0. 4 5 each. T he annual cost of the 900 Pl an i f no extr a mi nutes are used i s
( ) ( )
=59.99 12 $719.88
.
W e need to solve the foll owi ng equati on.
=
+=
=
≈
450 900
479.88 0.45 719.88
0.45 240
533
Pl an Cost Lowest Cost for Pl an
x
x
x
A s long as the total number of extr a mi nutes per year r emai ns at 5 33 mi nutes or below, the 45 0 Pl an i s
the least expensi ve of the two pl ans.
6. Which plan would you recommend to a consumer who expects to use between 400 and 600 minutes
each month? Explain your reasoning.
I f the consumer uses 4 50 mi nutes or less each month, the 450 Plan i s clear ly the better pl an. I n (5)
above, we saw that after 533 extra minutes annually (average of 44 minutes monthly), the 900 Plan
becomes the better value. I n other words, i f the consumer consi stentl y uses more than 494 mi nutes
monthl y, the 9 00 Pl an i s the better deal. I f the consumer i s on the 450 Plan and talks 600 minutes
each month, their annual cost is $1289.88! In contrast, the 900 Plan annual cost is $719.88. We
choose to play it safe and pick the 900 Plan.
Choosing a Cell Phone Plan-Verizon
Investigating Linear Equations
n 2008, Verizon offered the following cell phone plans to consumers. (Source: www.verizon.com)
Verizon: Nationwide Basic
Monthly Anytime Minutes Monthly Fee Charge for Extra Minutes
450 minutes $39.99 $0.45 per minute
900 minutes $59.99 $0.40 per minute
1350 minutes
$79.99
$0.30 per minute
1. If a customer expects to use 500 minutes per month, which plan is the best value?
450 Plan: $39.99 + (50 extra minutes)($0.45 per minute) = $62.49
900 Plan: $59.99
For this customer, the 900 minute plan costs less than the 450 minute plan.
2. A cell phone plan consists of a fixed cost (the monthly fee) and a variable cost (charge for extra
minutes). Find a linear function that gives the total cost of each plan when
x
extra minutes are used.
( )
( )
= +
= +
= +
()
()
Total Cost F i xed Cost V ari able Cost
Monthly Fee Cost per Extra Minute Extra Minute
Monthly Fee Cost per Extra Minute x
450 Plan:
= +39.99 0.45Cx
900 Plan:
= +59.99 0.40Cx
1350 Plan:
= +79.99 0.30Cx
3. Using the cost functions from (2) above, determine the cost of using 600 total minutes and 1000 total
minutes with each plan. Then determine which plan is the best deal for each level.
For the 450 Plan, 600 minutes requires 150 minutes more than the included minutes and 1000
mi nutes requi r es 55 0 mi nutes more than the included minutes. For the 900 Plan, 0 and 100 extra
mi nutes ar e needed, r especti vely. F or the 13 50 Pl an, no extra mi nutes are needed.
Plan 600 minutes 1000 minutes
450
39.99 0.45(150) $107.49
=+=39.99 0.45(550) $287.49C
900
=+=
59.99 0.40(0) $59.99C
*
=+=59.99 0.40(100) $99.99C
1350
=+=
79.99 0.30(0) $79.99C
=+=
39.99 0.30(0) $79.99C
*
I
4. The number of minutes a person uses each month often varies. Suppose that a Verizon customer uses
the total number of minutes shown below.
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
423 441 404 387 417 628 448 402 356 402 436 639
Which plan would cost the consumer the least amount money over the year?
Thi s consumer used less than 45 0 mi nutes a month ever y month except J une and December. In June,
they used 178 extra minutes and in December they used 189 extra minutes. In total, they used 367
extra minutes throughout the year. The basic fee for the 450 Plan is $39.99 per month so their annual
cost i s
( )
( )
( ) ( )
( ) ( ) ( ) ( )
= +
= +
= +
=
39.99 12 0.45 367
479.88 165.15
645.03
Annual Cost Monthly fee months cost per minute extra minutes
The annual cost for the 450 Plan is $645.03.
The 90 0 Plan costs $59. 99 per month for all 12 months for a total cost of $71 9. 8 8. E ven though the
consumer had to pay extr a duri ng June and December, the 45 0 Pl an was sti ll less expensi ve than the
900 Plan.
5.
At what number of extra minutes does the annual cost of the 900 Plan become less expensive than the
450 Plan?
The annual cost of the 450 Plan if no extra minutes are used is
( ) ( )
=39.99 12 $479.88
. Extra minutes
are $0. 4 5 each. T he annual cost of the 900 P lan i f no extra mi nutes are used i s
( ) ( )
=59.99 12 $719.88
.
W e need to solve the foll owi ng equati on.
=
+=
=
≈
450 900
479.88 0.45 719.88
0.45 240
533
Pl an Cost Lowest Cost for Pl an
x
x
x
A s long as the total number of extr a mi nutes per year r emai ns at 5 33 mi nutes or below, the 45 0 Pl an i s
the least expensi ve of the two plans.
6. Which plan would you recommend to a consumer who expects to use between 400 and 600 minutes
each month? Explain your reasoning.
I f the consumer uses 4 50 mi nutes or less each month, the 450 Plan i s clear ly the better pl an. I n (5)
a bove, we saw that after 533 extra minutes annually (average of 44 minutes monthly), the 900 Plan
becomes the better value. I n other words, i f the consumer consi stentl y uses more than 494 mi nutes
monthl y, the 9 00 Pl an i s the better deal. I f the consumer i s on the 450 Plan and talks 600 minutes
each month, their annual cost is $1289.88! In contrast, the 900 Plan annual cost is $719.88. We
choose to play it safe and pick the 900 Plan.
Worksheet Title
Choosing a Cell Phone Plan − Verizon
Filename:
m1001
Keywords
cell phone, Verizon, linear, model, fixed cost, variable cost, linear modeling, solving
equations
NCTM Standard
Content Standards Process Standards
Number and Operations
X
Problem Solving
X Algebra X Reasoning and Proof
Geometry X Communication
Measurement Connections
X Data Analysis and Probability Representations
Data Type
Table
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