A business owner registers 4 identical cell phone lines under a group plan. The service pr… — ACT

A business owner registers $4$ identical cell phone lines under a group plan. The service provider charges a monthly base fee of $\$15.00$ per line, plus $\$0.05$ per minute of call time. If the total monthly bill for all $4$ lines was $\$96.00$ and each line used the exact same number of minutes, how many minutes did each line use?

$180$ Answer
B
$405$
C
$720$
D
$31.5$
E
$1,620$

Answer

Each cell phone line used

180

minutes.

The correct answer is

180

minutes. The total bill for the

4

lines is represented by

4(15.00 + 0.05m) = 96.00

. Dividing both sides by

4

gives the monthly charge per line:

15.00 + 0.05m = 24.00

. Subtracting the base fee of

15.00

from both sides leaves the total per-minute cost of

0.05m = 9.00

. Dividing by the per-minute rate of

0.05

gives

m = 180

Step-by-Step Solution

Set up the linear equation representing the total monthly bill.

4(15.00 + 0.05m) = 96.00

, where

m

represents the number of minutes used per line.

The total bill is the sum of the charges for all

4

lines, where each line costs

\$15.00

plus

\$0.05

per minute.

Divide both sides of the equation by

4

to isolate the single-line cost expression.

15.00 + 0.05m = 24.00

Dividing both sides by

4

simplifies the equation and isolates the cost per line.

Subtract the base fee of

15.00

from both sides of the equation.

0.05m = 9.00

This isolates the variable charge term on the left side of the equation.

Divide both sides by

0.05

to solve for

m

m = 180

Dividing the remaining total of

9.00

by the rate of

0.05

per minute yields the total number of minutes used.

Key Concept

Solving Linear Equations

Alternative Method

Instead of dividing by

4

first, distribute the

4

to both terms inside the parentheses:

4(15.00) + 4(0.05m) = 96.00

. This simplifies to

60.00 + 0.20m = 96.00

. Subtract

60.00

from both sides to get

0.20m = 36.00

. Finally, divide by

0.20

to find

m = 180

Estimated Time:1m 15s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Alternative Method

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