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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?

 Jun 13, 2021
edited by bossboy1335  Jun 13, 2021
 #1
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                                            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.  

.

 Jun 13, 2021
 #2
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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 . 

 

 Jun 13, 2021
edited by Bginner  Jun 13, 2021

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