The problem describes Alan working as a tutor for $9 an hour and as a waiter for $8 an hour. He worked a total of 105 hours combined for both jobs. We need to express his total earnings.

Let:

• $t$ be the number of hours Alan worked as a tutor.
• $105 - t$ be the number of hours Alan worked as a waiter (since the total hours worked is 105).

The total earnings are calculated by adding his earnings from both jobs:

1. His earnings from tutoring: $9t$ dollars (since he earns $9 for each hour).
2. His earnings from waiting: $8(105 - t)$ dollars (since he earns $8 for each hour and worked $105 - t$ hours as a waiter).

The expression for the total earnings is: $9t + 8(105 - t)$

You can simplify this further: $9t + 8(105 - t) = 9t + 840 - 8t = t + 840$

So, the combined total dollar amount he earned this month is given by: $t + 840$

Would you like further details or explanations?

Here are some related questions:

1. How many hours did Alan work as a tutor if he earned $900 in total?
2. What is the maximum amount Alan could have earned if he only worked as a tutor?
3. If Alan worked 40 hours as a waiter, how much did he earn from both jobs combined?
4. How many hours must Alan work as a tutor to earn at least $500?
5. What is the minimum number of hours Alan can work to make at least $1000?

Tip: When forming algebraic expressions, ensure that all the parts of the equation represent real-world situations accurately for clarity.