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QLT1 Task 1 Rev 1

QLT1 Task 1

Mary is going away to college. In order to stay in touch with her family and friends she needs to get a cell phone with a calling plan. At this time Mary isn’t sure what her monthly phone usage is going to be. After consulting with her college friends, she estimates her usage will be between 200 and 900 minutes per month.

A local phone company offers two basic calling plans:

Plan A. offers a package consisting of monthly charge of $50.00 and $0.10 for each minute. Plan B. offer is a monthly fee of $15.00 and $0.18 per minute.

The phone company charges for actual time used for both plans, so if Mary used .75 Min for talk time she would pay for actual time used [(.75) x per minute rate]

Plan A

The cost of plan (Y)

X= phone usage in minutes (this is our variable)

Y=50 + 0.10(x). The cost of plan A (Y) is $50 base charge plus $.10 per each minute (x) represented in a linear equation.

Plan B

X= phone usage in minutes (this is our variable)

Y=15 + .18(x). The cost of plan B (Y) is $15 base charge plus $.18 per each minute (x) represented in a linear equation.

1. Which plan would offer greater savings if Mary’s monthly phone usage was 200 min?

Plan A

Cost of phone plan after using 200 minutes.

Y=50 + .10(x)

X 200

Y=50 + .10(200)

Y=50 + 20

Y=70

Plan A would cost Mary $70 per month after 200 minutes usage

Plan B

Cost of phone plan after using 200 minutes

Y=15 + .18(x)

X 200

Y=15 + .18(200)

Y=15 + 36

Y=51

Plan B Would Cost Mary $51 per month after 200 minutes usage.

Answer: Plan B would be more advantageous for Mary at $51 per month over Plan A at $70 per month after 200 minutes of usage.

2. Which Plan would offer Mary greatest savings if her monthly usage was 900 min?

Cost of phone plan A after using 900 minutes

Y=50+.10(x)

X 900

Y=50+.10(900)

Y=50+90

Y=140

Plan A would cost Mary $140 per month after 900 minutes usage

Cost of phone plan B after using 900 minutes

Y=15+.18(x)

X 900

Y=15+.18(900)

Y=15+162

Y=177

Plan B would cost Mary $177 per month after 900 minutes usage

Answer: Plan A at $140 per month would offer Mary greater savings.

3. After how many minutes of usage the cost for both plans would be equal?

50+ .10(x) =15+ .18(x) move like numbers from one side of the equation to the other with opposite sign.

50-15= .18(x) - .10 (x)

35=.08(x) divide both sides .08 to extract the value of x

437.5=x

Answer: Both plans would cost the same after 437.5 minutes of usage.

Cost of plan A after 437.5 minutes of usage.

Y=50+.10(x)

Y=50+.10(437.5)

Y=50+43.75

Y=93.75

Cost of plan B after 437.5 minutes of usage.

Y=15+.18(x)

Y=15+.18(437.5)

Y=15+78.75

Y=93.75

Graphical depiction of the above situation.

Plan A Plan B

X y x y

0 50 0 15 200 70 200 51 437.5 93.75 437.5 93.75 900 140 900 177

Plan B would be most advantageous if Mary’s calling time remains under 437.5 minutes per month at which point the monthly cost for both plans is the same. However, if she exceeded 437.5 minutes per month Plan A would make more sense since the cost of plan B drastically increases with additional time over 437.5 minutes.…...

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