Question

You need to purchase a new cell phone plan. Company A offers 700 minutes of talk time per month but they charge 15 cents for every minute you go over the 700 included minutes. Company A will charge you $40 per month for this plan. Company B offers 500 minutes of talk time per month, but they charge only 5 cents per minute for exceeding the 500 minutes. Company B charges $50 per month for this plan. At what number of minutes per month would both plans charge the same amount?

Answer 1

Both plans would charge the same amount when 900 minutes per month are used.

Explanation:

Plan A: 700 free minutes + 15 cents per minute over 700 ($40)

Plan B: 500 free minutes + 5 cents per minute over 500 ($50)

1 cent = 0.01$

15 cent = 0.15$

5 cents = 0.05$

The charges for x minutes (assumed x>700) for plan A will be

40+0.15(x-700)

The charges for x minutes (assumed x>500) for plan B will be

50+0.05(x-500)

To find the value of x where both charges are the same, we equate

`40+0.15(x-700)=50+0.05(x-500)\\40+0.15x-105=50+0.05x-25\\0.15x-0.05x=25+75\\0.1x=90\\x=(90)/(0.1) =900 mins`

Hence,both plans would charge the same amount when 900 minutes per month are used.