Question

A phone company has a monthly cellular plan where a customer pays a flat monthly fee and then a certain amount of money per minute used on the phone. If a customer uses 410 minutes, the monthly cost will be $71.50. If the customer uses 720 minutes, the monthly cost will be $118. Find a linear equation for the monthly cost of the cell plan as a function of x, the number of monthly minutes used.

Answer 1

Linear equation for the monthly cost of the cell plan is
`10+0.15x`

Explanation:

Let u denotes a flat monthly fee and v denotes amount charged per minute.

As the monthly cost is $71.50 if a customer uses 410 minutes,

`71.50=u+410v` (i)

As the monthly cost is $118 if a customer uses 720 minutes,

`118=u+720v` (ii)

Subtract (i) from (ii)

`118-71.50=u+720v-u-410v\\46.5=310v\\v=(46.5)/(310)\\ v=0.15`

Put
`v=0.15` in (i)

`71.50=u+410(0.15)\\71.50=u+61.5\\u=71.50-61.5\\u=10`

As x denotes the number of monthly minutes used,

linear equation for the monthly cost of the cell plan is
`10+0.15x`