Groan works as a tutor for $13 an hour and as a waiter for $12 an hour. This month, he worked a combined total of 109 hours at this two jobs. Let t be the number of hours Groan worked as a tutor this month. Write an expression for the combined total dollar amount he earned this month.

Answer 1

To find the total dollar amount Groan earned this month from both jobs, we can set up an expression based on the number of hours he worked as a tutor and a waiter.

Let:

• \( t \) = number of hours Groan worked as a tutor
• \( w \) = number of hours Groan worked as a waiter

From the problem statement, we know that:

• The hourly pay for tutoring is $13,
• The hourly pay for waiting is $12,
• The total number of hours worked at both jobs is 109 hours.

We can express the number of hours worked as a waiter in terms of \( t \): \[ w = 109 - t \]

Now, we can express the total earnings from both jobs:

1. Earnings from tutoring: \( 13t \)
2. Earnings from waiting: \( 12w = 12(109 - t) \)

Now, putting it all together, the total earnings \( E \) can be expressed as: \[ E = 13t + 12(109 - t) \]

Now, let's simplify this expression: \[ E = 13t + 12 \times 109 - 12t \] \[ E = (13t - 12t) + 1308 \] \[ E = t + 1308 \]

Therefore, the expression for the combined total dollar amount Groan earned this month is: \[ E = t + 1308 \]