When pedro called Gary, the call cost $1.58. If the rate for the call was 53 cents for the first three minutes and 15 cents for each additional minute or fraction thereof, how long did Pedro and gary talk?

.53 + .15[m-3] = 1.58

.15[m-3] = 1.05
[m-3] = 7
m-3 = 7
m = 10

check:

.53 + .15*7 = .53 + 1.05 = 1.58

To determine how long Pedro and Gary talked, we'll calculate the duration of the call based on the given information.

Let's break down the cost of the call and use it to find the duration:

1. The rate for the call was 53 cents for the first three minutes.
- This means that Pedro and Gary were charged 53 cents for the first three minutes of the call.
- So, the cost of the call for the remaining duration would be $1.58 - $0.53 = $1.05.

2. The rate for each additional minute (beyond the first three minutes) was 15 cents.
- This implies that for every minute or fraction thereof after the initial three minutes, Pedro and Gary were charged 15 cents.
- Therefore, we need to calculate how many minutes are covered by the remaining $1.05.

Next, divide the remaining cost ($1.05) by the rate per minute ($0.15) to find the number of additional minutes:

$1.05 / $0.15 = 7

This calculation tells us that Pedro and Gary were charged for an additional 7 minutes of talk time after the initial three minutes.

The total duration of the call is the sum of the initial three minutes and the additional seven minutes:

Total duration = 3 minutes + 7 minutes = 10 minutes

Therefore, Pedro and Gary talked for 10 minutes.