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

Question

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

Answer 1

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 2

in y = mx + b form

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: \[ y = 0.05x + 40 \]