Final answer:
After setting up an equation based on the pricing structure of the telephone company, and solving for the total number of minutes a person can talk for $25, the interval representing the talk time is 0 ≤ x ≤ 171 minutes, which corresponds to option d.
Step-by-step explanation:
To determine the interval that represents how long a person can talk on the phone for $25, we need to set up an equation based on the pricing structure of the telephone company. The charge is $0.75 for the first 10 minutes and $0.15 for each additional minute. Let's denote the total number of minutes talked as x.
For the first 10 minutes, the cost is $0.75. After the first 10 minutes, each additional minute costs $0.15. If the total cost is $25, we deduct the initial charge from the total amount and then divide by the cost per additional minute to find the number of additional minutes.
The equation representing this scenario is:
0.75 + 0.15(y - 10) = 25
where y represents the total minutes. Solving for y gives us the total number of minutes the person can talk. Here's how to calculate it:
0.75 + 0.15(y - 10) = 25
0.15(y - 10) = 25 - 0.75
y - 10 = (24.25 / 0.15)
y = (24.25 / 0.15) + 10
y ≈ 171.67
Since a person cannot talk for a fraction of a minute, we round down to the nearest whole number, which is 171. Thus, the interval representing how a person can talk for $25 is 0 ≤ x ≤ 171 minutes, matching option d.