Question

A mobile phone company offers two monthly calling plans, A and B. Under A, every minute costs $ 0.10. Under B, the first 100 minutes costs $ 12 and every extra minute costs $ 0.08. What monthly talking time would make B the better choice?

Answer 1

A 1min = $0.10
A 100min = $0.10 x 100 = $10
B 100min = $12
B-A = $2
101th min onwards:
A 1 min = $0.10
B 1 min = $0.08
A-B = $0.02

$2 / $0.02 = 100 min
A 200 min = $0.10 x 200 = $20
B 200 min = $12 + ($0.08 x 100) = $20

A 201 min = $20.10
B 201 min = $20.08

Monthly talking time should be 201 minutes and above for B to be the better choice

Answer 2

x - talking time in minutes
y - price

A:

`y=0.1x`

B:

`y=12+(x-100)\cdot0.08 \\ y=12+0.08x-8 \\ y=0.08x+4`

B price must be less than A so:

`0.08x+4 < 0.1x \\ 4 < 0.1x-0.08x \\ 4 < 0.02x \\ 200 < x \\ x>200`

More than 200 minutes of talking would make B the better choice.