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

Answer:

1022 minutes

Step-by-step 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

$\frac{4\left(x-900\right)}{4}=\frac{488}{4}$

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