after how much time, to the nearest minute, will the cost of plan a be equal to the cost plan b

Question

Plan a charges $11 a month and $0.21 per minute.plan b charges $20 a month and $0.10 per minute

 

Answer 1

Let x=number of minutes

 

Plan a:

    Cost_a = $11.00 + $0.21x

Plan b:

    Cost_b = $20.00 + $0.10x

 

When does Cost_a = Cost_b ?

    11.00 + 0.21x = 20.00 + 0.10x

      0.11x = 9.00

        x= 81.82

        x= 82 minutes    (rounded to the nearest minute)

 

Checking (very important):

  Is   11+0.21(82) ≈ 20+0.10(82)  ?

        28.22  ≈ 28.18   ? yes

Answer 2

m represents the number of minutes

 

11 + 0.21m = 20 + 0.10m            subtract 11 from both sides

0.21m = 9 + 0.10m                       subtract 0.10m from both sides

0.01m = 9                                     divide both sides by 0.01

m = 900

 

The two plan have equal cost at 900 minutes.