Dan is trying to find a new cell phone plan. Throttle Talks offers a plan for $64.41 a month, plus $2.00 for each megabyte of data. Clutch Cells offers a plan for $63.91 a month, plus $2.05 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

OA. 5

OB. The cost will never be the same.

OC. 7.9

OD. 10

Answer 1

To find the number of megabytes of data that will make both cell phone plans cost the same, we can set up an equation based on the given costs.

Let \( x \) be the number of megabytes of data Dan uses in a month.

The total cost for Throttle Talks can be expressed as: \[ \text{Cost}_{\text{Throttle Talks}} = 64.41 + 2.00x \]

The total cost for Clutch Cells can be expressed as: \[ \text{Cost}_{\text{Clutch Cells}} = 63.91 + 2.05x \]

We want to find the value of \( x \) where these costs are equal: \[ 64.41 + 2.00x = 63.91 + 2.05x \]

Now, let's simplify the equation:

1. Subtract \( 2.00x \) from both sides: \[ 64.41 = 63.91 + 0.05x \]

2. Now subtract \( 63.91 \) from both sides: \[ 64.41 - 63.91 = 0.05x \]

3. This simplifies to: \[ 0.50 = 0.05x \]

4. Now, divide both sides by \( 0.05 \): \[ x = \frac{0.50}{0.05} = 10 \]

So, the number of megabytes of data Dan will have to use in one month for the cell phone plans to cost him the same amount is 10 megabytes.

The correct answer is: OD. 10