Answer:
Plan A equation: y = 10x + 30
Plan B equation: y = x + 80
Plan C equation: y = 5x + 50
Plan A costs the same as Plan C in 4 months
Plan A is the better option if you use 0 - 4 GBs of data each month
Plan B becomes the better deal when 8 months pass
Step-by-step explanation:
<u>When does Plan A cost the same as Plan C?</u>
Set the equations equal to each other (the cost) and solve for x (time in months)
10x + 30 = 5x + 50
5x = 20
x = 4 months
<u>Which plan is best if you only use 0-4 GBs of data a month?</u>
Test the maximum and minimum values to check which plan costs less
At 0 GBs of data used per month
Plan A: y = 0 + $ 30 = $30 total
Plan B: y = 0 +$80 = $80 total
Plan C: y = 0 + $50 = $50 total
At 4 GBs of data used per month
Plan A: y = $ 40 + $ 30 = $ 70
Plan B: y = $ 4 + $ 80 = $ 84
Plan C: y = $ 20 + $ 50 = $ 70
Comparing the plans at maximum and minimum amount of GBs used, only one plan has the lowest cost overall. Even though Plan C is the same price at 4 GBs as Plan A, when you use 0 GBs you will end up paying more in Plan C than Plan A. Therefore, Plan A is the better option
<u>When does Plan B become the best deal?</u>
When you plot the different Plans on a graph, the slope intercept of x = 7.5 (rounded up to 8) yields the lowest cost for plan B
multiples of 7 between 0 and 100, so there is a 
probability of choosing a multiple of 7.