Question

The cellular phone service for a business executive is $35 per month plus $0.40 per minute of phone use over 900 min. For amonth in which the executive's cellular phone bill was $83.80, how many minutes did the executive use the phone?

Answer 1

1022 minutes

Explanation:

Let x be the number of minutes the executive used the phone

There is a base charge of $35 and only minutes greater than 900 min are charged at the rate of $0.40 per minute

So total bill A = 35 + 0.4(x-900)

We know the bill was $83.80

So we can rewrite the equation as

35 + 0.4(x-900) = 83.30

and solve for x

To make it easier for computational purposes

1) Multiply both sides by 10

`35\cdot \:10+0.4\left(x-900\right)\cdot \:10=83.8\cdot \:10`

2) Perform individual multiplication

`350+4\left(x-900\right)=838`

3) Subtract 350 from both sides

`350+4\left(x-900\right)-350=838-350`

4) Simplify

`4\left(x-900\right)=488`

5) Divide both sides by 4

`(4\left(x-900\right))/(4)=(488)/(4)`

6) Simplify

`x-900=122`

7) Add 900 to both sides to isolate x

`x-900+900=122+900`

8) Simplify to obtain x

`x=1022`

Answer: The executive used the phone for 1022 minutes that month