Questions: Nick traveled out of the country for a month. He purchased a plan from his cell phone company that would allow him to send text messages to friends and family back home. Nick's telephone company charges 0.40 for a regular text message and 0.70 for a multimedia text messages. This month Nick was billed 99 and he sent a total of 195 messages. How many regular text messages and multimedia text messages did he send? The number of regular text messages sent was and the number of multimedia text messages sent was 7.

Nick traveled out of the country for a month. He purchased a plan from his cell phone company that would allow him to send text messages to friends and family back home. Nick's telephone company charges 0.40 for a regular text message and 0.70 for a multimedia text messages. This month Nick was billed 99 and he sent a total of 195 messages. How many regular text messages and multimedia text messages did he send? The number of regular text messages sent was and the number of multimedia text messages sent was 7.
Transcript text: Nick traveled out of the country for a month. He purchased a plan from his cell phone company that would allow him to send text messages to friends and family back home. Nick's telephone company charges $\$ 0.40$ for a regular text message and $\$ 0.70$ for a multimedia text messages. This month Nick was billed $\$ 99$ and he sent total of 195 messages. How many regular text messages and multimedia text messages did he send? The number of regular text messages sent was $\square$ and the number of multimedia text messages sent was $\square$ 7.
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Solution

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Solution Steps

Step 1: Set Up the Equations

To find the number of regular and multimedia text messages Nick sent, we set up a system of linear equations based on the given information. Let \( r \) represent the number of regular text messages and \( m \) represent the number of multimedia text messages.

  1. The total cost equation is: \[ 0.40r + 0.70m = 99 \]

  2. The total number of messages equation is: \[ r + m = 195 \]

Step 2: Solve the System of Equations

We solve the system of equations to find the values of \( r \) and \( m \).

  1. From the second equation, express \( r \) in terms of \( m \): \[ r = 195 - m \]

  2. Substitute \( r = 195 - m \) into the first equation: \[ 0.40(195 - m) + 0.70m = 99 \]

  3. Simplify and solve for \( m \): \[ 78 - 0.40m + 0.70m = 99 \] \[ 0.30m = 21 \] \[ m = \frac{21}{0.30} = 70 \]

  4. Substitute \( m = 70 \) back into the equation for \( r \): \[ r = 195 - 70 = 125 \]

Final Answer

\(\boxed{r = 125, \, m = 70}\)

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