Question

Dan is trying to find a new cell phone plan. Throttle Talks offers a plan for $64.09 a month, plus $1.95 for each megabyte of data. Clutch Cells offers a plan for $63.59 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?
A.
7.7
B.
5
C.
10
D.
The cost will never be the same.

Answer 1

To find the number of megabytes of data at which both cell phone plans cost the same amount, we can set up an equation based on the given monthly fees of both plans.

Let \( x \) be the number of megabytes of data used in one month.

The total cost for Throttle Talks is:
\[
64.09 + 1.95x
\]

The total cost for Clutch Cells is:
\[
63.59 + 2.00x
\]

We want to find \( x \) such that the costs are equal:
\[
64.09 + 1.95x = 63.59 + 2.00x
\]

Now, let's solve for \( x \):
1. Subtract \( 1.95x \) from both sides:
\[
64.09 = 63.59 + 0.05x
\]

2. Subtract \( 63.59 \) from both sides:
\[
64.09 - 63.59 = 0.05x
\]
\[
0.50 = 0.05x
\]

3. Divide both sides by \( 0.05 \):
\[
x = \frac{0.50}{0.05} = 10
\]

Thus, Dan will have to use **10 megabytes of data** for the cell phone plans to cost him the same amount.

**The answer is C. 10**.