Let's break down this problem.
Firstly, we know that Kathy's total phone bill last month was $110. We also know that there's a base fee of $50 that the phone company charges every month, whether or not the phone is used.
We need to find out how much of Kathy's bill was for the actual call charges. So, we can subtract the base fee from the total cost of the bill.
110 (Kathy's total bill) - 50 (base fee) = $60.
So, Kathy paid $60 for the actual phone usage.
Next, we are given that the cost per minute of phone usage is $0.10. So, we need to find out how many minutes Kathy was on the call.
To find out that, we can divide the cost of phone usage by the cost per minute.
60 (cost of phone usage) / 0.10 (cost per minute) = 600 minutes.
So, Kathy spent 600 minutes on the phone last month according to her father's checkbook.
Our answer is that Kathy spent 600 minutes on the phone last month.