# Which Plan should Smith buy?

## The situation(cost/extra minute)

Smith wants to buy a cellular plan for his new phone. He wants see which plan is better for the cost per extra minute. He contacts two big companies, Bell and Telus to find their plans. Both the plans start at a 150 mins. free per month with the plan and extra money for each extra minute he talks. The amount of data and texting are exactly the same but the costs are different for calling in the plan. He decides to graph the data.

## The variables

Independent Variable in this case is minutes(x) and the dependent variable is cost(y). The number of minutes Smith uses determines the cost.

y represents the number of minutes

x represents the cost

## The equations in slope y-intercept form

y=mx+b

y=0.6x+30.75

rate of change:0.6x first difference(6/10)

constant:30.75

y=mx+b

y=0.5x+35

rate of change:0.5 first difference (5/10)

constant:35

## The standard form

Bell:

y=0.6x+30.75

100(0.6x-y+30.75)=100(0) Multiply by 100 to get rid of the decimals and

60x-100y+3075=0 subtracted y from both sides.

standard form: 60x-100y+3075=0 or 60x-100y=-3075

Telus:

y=0.5x+35

10(0.5x-y+35)=10(0) Subtracted y from both sides and multiplied by 10 to get rid of the

5x-10y+350 decimals.

standard form: 5x-10y+350=0 or 5x-10y=-350

## The graph

the lines:

-Bell:Blue line

-Telus:Red line

P.O.I.:(42.5,56.25) At 42.5 minutes the cost for both companies is \$56.25.

## Using equations to solve the P.O.I.

0.6x+30.75=0.5x+35

0.6x-0.5x=35-30.75 Rearranging to group like terms

0.1x=4.25 Isolating x

x=42.5

Plug x into any equation, because at this point both points have the same x and y value.

y=0.5x+35

y=0.5(42.5)+35

y=21.25+35

y=56.25

P.O.I.:(42.5,56.25)

## Significance of the linear system

The graph and the data tell us that which plan is better at what circumstances. Based on the graph it tells Smith that if more than 42.5 extra minutes are being used per month then it is better to with Telus because it is much cheaper as we extrapolate the data but when less than 42.5 minutes are used then it's best to go with Bell because it is much cheaper.

## Conclusion

At 42.5 extra minutes both companies will have the same cost 56.25 dollars. It's up to Smith to decide which plan is better.

Bell is better when he uses less than 192.5 minutes per month (150 minutes+42.5 minutes), while Telus is better when he goes over than 192.5 minutes per month.