2.) A monthly cell phone plan charges $5.00 for the first 300 text messages used and $0.15 for each additional
message. On this plan, what is the number of text messages that must be used in a month in order to make the
average cost per message $0.05 ?
a. 400
c. 900
b. 350
d. 500
To find the number of text messages that must be used in a month in order to make the average cost per message $0.05, we can set up an equation.
Let's denote the number of additional messages as "x".
According to the given information, the cost for the first 300 messages is $5.00, and the cost for each additional message is $0.15.
The total cost for the additional messages will be 0.15 * x.
The total cost for all the messages (including the first 300) will be $5.00 + 0.15 * x.
The average cost per message is the total cost divided by the total number of messages: (5.00 + 0.15 * x) / (300 + x).
We can set up the equation:
(5.00 + 0.15 * x) / (300 + x) = 0.05.
To solve this equation, we can cross-multiply:
5.00 + 0.15 * x = 0.05 * (300 + x).
Expanding the equation:
5.00 + 0.15 * x = 15 + 0.05 * x.
Combining like terms:
0.1 * x = 10.
Dividing both sides of the equation by 0.1:
x = 100.
Therefore, the number of additional messages (x) that must be used in a month to make the average cost per message $0.05 is 100.
The total number of messages will be the sum of the first 300 messages and the additional messages:
300 + 100 = 400.
Therefore, the correct answer is (a) 400.
350
To find the number of text messages that must be used in a month in order to make the average cost per message $0.05, we need to calculate the total cost of the plan for different numbers of messages and find the number of messages that results in an average cost of $0.05.
Let's start by calculating the total cost for 350 messages:
- The first 300 messages cost $5.00.
- For the remaining 50 messages, the cost is $0.15 per message. So, 50 messages * $0.15 = $7.50.
- The total cost for 350 messages is $5.00 + $7.50 = $12.50.
For 400 messages:
- The first 300 messages cost $5.00.
- For the remaining 100 messages, the cost is $0.15 per message. So, 100 messages * $0.15 = $15.00.
- The total cost for 400 messages is $5.00 + $15.00 = $20.00.
For 500 messages:
- The first 300 messages cost $5.00.
- For the remaining 200 messages, the cost is $0.15 per message. So, 200 messages * $0.15 = $30.00.
- The total cost for 500 messages is $5.00 + $30.00 = $35.00.
For 900 messages:
- The first 300 messages cost $5.00.
- For the remaining 600 messages, the cost is $0.15 per message. So, 600 messages * $0.15 = $90.00.
- The total cost for 900 messages is $5.00 + $90.00 = $95.00.
As we can see, none of these options result in an average cost of $0.05.
Thus, the correct answer is none of the given options.