Dan is trying to find a new cell phone plan. Throttle Talks offers a plan for $64.72 a month, plus $1.95 for each megabyte of data. Clutch Cells offers a plan for $64.22 a month, plus $2.00 for each megabyte of data. How many megabytes of data will Dan have to use in one month for the cell phone plans to cost him the same amount?

Question

A.
10
B.
The cost will never be the same.
C.
7.7
D.
5

Answer 1

Let's define the cost of each cell phone plan as a function of the number of megabytes of data used, denoted as \( x \).

Throttle Talks: \[ \text{Cost} = 64.72 + 1.95x \]

Clutch Cells: \[ \text{Cost} = 64.22 + 2.00x \]

To find the number of megabytes \( x \) at which the costs are equal, we set the two equations equal to each other:

\[ 64.72 + 1.95x = 64.22 + 2.00x \]

Next, we can begin solving for \( x \):

1. Subtract \( 1.95x \) from both sides:

\[ 64.72 = 64.22 + 2.00x - 1.95x \]

This simplifies to:

\[ 64.72 = 64.22 + 0.05x \]

2. Now subtract \( 64.22 \) from both sides to isolate \( x \):

\[ 64.72 - 64.22 = 0.05x \]

\[ 0.50 = 0.05x \]

3. Divide both sides by \( 0.05 \):

\[ x = \frac{0.50}{0.05} = 10 \]

Thus, Dan would have to use 10 megabytes of data for both plans to cost him the same amount.

The answer is:

A. 10