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# PLS ANYONE of you geniusess

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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

### 2+0 Answers

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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.

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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