The cost for a long-distance telephone call is $0.36 for the first minute and $0.21 for each additional minute or portion thereof. Write an inequality representing the number of minutes a person could talk without exceeding $3.
Well, Cost= .36 + (minutes-1)(.21)
Does that help?
Yes, that is the correct formula to calculate the cost of a call. Now, we need to set up an inequality representing the number of minutes a person could talk without exceeding $3.
Let m represent the number of minutes talked. So, the inequality should look like this:
0.36 + (m - 1) * 0.21 ≤ 3
Yes, your equation for the cost is correct. However, to represent the number of minutes a person could talk without exceeding $3, we need to set up an inequality.
Let's assume the number of minutes a person could talk is represented by "m".
The cost for the first minute is $0.36, and for each additional minute or portion thereof, it is $0.21. So, for m minutes, excluding the first minute, the cost would be (m - 1) * $0.21. Adding the cost of the first minute, the total cost would be $0.36 + (m - 1) * $0.21.
To write an inequality stating that the total cost should not exceed $3, we can set up the following equation:
$0.36 + (m - 1) * $0.21 ≤ $3
To explain how to solve this inequality, we'll isolate the variable m:
$0.36 + (m - 1) * $0.21 ≤ $3
$0.36 + $0.21m - $0.21 ≤ $3
$0.21m - $0.21 ≤ $3 - $0.36
$0.21m ≤ $2.64
Next, we divide both sides of the inequality by $0.21 to solve for m:
$\frac{{0.21m}}{{0.21}} ≤ \frac{{2.64}}{{0.21}}
m ≤ 12.57
Therefore, the number of minutes a person could talk without exceeding $3 is less than or equal to 12.57, which we can round down to 12.
So the inequality representing the number of minutes a person could talk without exceeding $3 is m ≤ 12.
Almost! The formula you provided is correct, but to write the inequality representing the number of minutes a person could talk without exceeding $3, we need to set up a limit for the cost.
Let's call the number of minutes the person talks "x". The cost of the first minute is $0.36, and the cost of each additional minute is $0.21. So the total cost of the call is:
Total cost = $0.36 + ($0.21)(x-1)
To represent the inequality, we want the total cost to be less than or equal to $3. So we can write:
$0.36 + ($0.21)(x-1) ≤ $3
This can also be written as:
0.36 + 0.21x - 0.21 ≤ 3
Simplifying further:
0.15 + 0.21x ≤ 3
Now we can solve for x:
0.21x ≤ 3 - 0.15
0.21x ≤ 2.85
x ≤ 2.85 / 0.21
x ≤ 13.57
Therefore, the inequality representing the number of minutes a person could talk without exceeding $3 is x ≤ 13.57.