Question

VoiceStream offered a plan for $40 per month, plus an additional charge of 5 cents for every text sent.

If you send 100 text messages in a month, what would your total monthly cost be?
Explain

Answer 1

in y = mx + b form

Answer 2

To calculate the total monthly cost for the VoiceStream plan, we start with the base monthly fee and then add the cost of the text messages sent.

1. **Fixed Monthly Fee**: $40

2. **Cost of Text Messages**:
- The charge per text message is 5 cents, which can be converted to dollars:
\( 5 \text{ cents} = 0.05 \text{ dollars} \).
- If you send 100 text messages, the total cost for the text messages will be:
\( 100 \text{ messages} \times 0.05 \text{ dollars/message} = 5 \text{ dollars} \).

3. **Total Monthly Cost**:
- Now, add the fixed monthly fee and the cost of the text messages:
\( 40 \text{ dollars} + 5 \text{ dollars} = 45 \text{ dollars} \).

Therefore, if you send 100 text messages in a month, your total monthly cost would be **$45**.

Answer 3

To express the cost of the plan in the form of \( y = mx + b \), let's define the variables:

- Let \( y \) be the total monthly cost.
- Let \( x \) be the number of text messages sent.
- Let \( m \) be the variable cost per text message.
- Let \( b \) be the fixed monthly fee.

From the problem:

- The fixed monthly cost (the base fee) is \( b = 40 \) dollars.
- The cost per text message is \( m = 0.05 \) dollars (which is 5 cents).

The equation calculating the total monthly cost based on the number of text messages sent is:

\[
y = mx + b
\]

Substituting in the values for \( m \) and \( b \):

\[
y = 0.05x + 40
\]

In this equation:
- \( y \) is the total monthly cost,
- \( x \) is the number of text messages sent,
- \( 0.05 \) is the cost per text message, and
- \( 40 \) is the fixed monthly fee.

So, the cost in \( y = mx + b \) form is:
\[
y = 0.05x + 40
\]