Bob is trying to decide between two cell phone plans. Plan A has no flat fee, but the user must pay $10$ cents per minute on the phone. Plan B requires a one-time fee of $\$20$, but only requires a payment of $5$ cents per minute on the phone. What is the minimum whole number of minutes Bob has to use the phone for to make Plan B the cheaper plan?
Plan A Plan B
Cost for 100 minutes (¢) 1,000 2,000 + 500 = 2,500
Cost for 200 minutes (¢) 2,000 2,000 + 1,000 = 3,000
Cost for 300 minutes (¢) 3,000 2,000 + 1,500 = 3,500
Cost for 400 minutes (¢) 4,000 2,000 + 2,000 = 4,000
You can see that, starting with the 401st minute, Plan B is the cheaper plan.
Key idea: : Let y = Total paid for Plan A = B , at x minutes use
we compare two equations of plan A & B and solve for x minutes use
Plan A : y = 0.10 x
Plan B: y = (0.05)x + 20
0.10x = (0.05)x + 20
x = 400
(Meaning: Plan B will be cheaper after 400 min. )
At x = 400 is the intercept between Plan A and B. The slope of Plan B is increase slower than the Plan A
Red line y = (0.05)x + 20 .