For a long-distance person-to-person telephone call, a telephone company charges $ 0.51 for the first minute, $ 0.34 for each additional minute, and a $ 2.06 service charge. If the cost of a call is $ 6.65 comma how long did the person talk?
6.65 = 2.06 + 0.51 + 0.34 * (t-1)
Let's denote the number of additional minutes the person talked as "x".
Given:
Cost of the first minute: $0.51
Cost of each additional minute: $0.34
Service charge: $2.06
Total cost of the call: $6.65
We can create an equation to represent the total cost of the call:
Total Cost = Cost of the first minute + Cost of additional minutes + Service charge
$6.65 = $0.51 + ($0.34 * x) + $2.06
Now, we can solve this equation to find the value of "x" (the number of additional minutes the person talked):
$6.65 - $0.51 - $2.06 = $0.34 * x
$4.08 = $0.34 * x
x = $4.08 / $0.34
x = 12
Therefore, the person talked for 12 additional minutes.
To find out the duration of the person's call, we can set up an equation using the given information. Let's break it down step by step:
Let's denote the duration of the call in minutes as 'x'.
The first minute of the call costs $0.51, and each additional minute costs $0.34. So, the cost of the call excluding the service charge can be calculated as:
Cost of additional minutes = (x - 1) * $0.34
Adding the service charge of $2.06, the total cost of the call can be expressed as:
Total cost = Cost of first minute + Cost of additional minutes + Service charge
Total cost = $0.51 + (x - 1) * $0.34 + $2.06
Now, we can set up an equation using the given total cost of $6.65:
$6.65 = $0.51 + (x - 1) * $0.34 + $2.06
To solve for 'x', let's simplify the equation:
$6.65 = $0.51 + $0.34x - $0.34 + $2.06
$6.65 = $0.51 + $0.34x + $2.06 - $0.34
Combining like terms:
$6.65 - $2.06 - $0.51 + $0.34 = $0.34x
$4.08 = $0.34x
Divide both sides by $0.34:
$4.08 / $0.34 = x
12 = x
Therefore, the person talked for 12 minutes.