Question

Josh works as a tutor for $11
an hour and as a waiter for $15
an hour. This month, he worked a combined total of 106
hours at his two jobs.

Let t
be the number of hours Josh worked as a tutor this month. Write an expression for the combined total dollar amount he earned this month.

Answer 1

To create an expression for the combined total dollar amount Josh earned this month, we can break down his earnings from both jobs using the variable \( t \) (the number of hours worked as a tutor).

1. **Tutoring Earnings**: Josh earns $11 for each hour he works as a tutor. If he worked \( t \) hours, his earnings from tutoring would be:
\[
11t
\]

2. **Waiting Earnings**: Josh also works as a waiter and earns $15 for each hour he works. The total number of hours he worked at both jobs is 106 hours. Therefore, the number of hours he worked as a waiter can be expressed as:
\[
106 - t
\]
(since the total hours worked is 106, the hours worked as a waiter is the total hours minus the hours worked as a tutor).

His earnings from waiting can therefore be expressed as:
\[
15(106 - t)
\]

3. **Combined Earnings**: To find his total earnings from both jobs, we combine his tutoring earnings and waiting earnings:
\[
\text{Total Earnings} = 11t + 15(106 - t)
\]

Now, simplifying that expression gives:
\[
\text{Total Earnings} = 11t + 15 \times 106 - 15t
\]
\[
= 11t + 1590 - 15t
\]
\[
= (11t - 15t) + 1590
\]
\[
= -4t + 1590
\]

Thus, the expression for the combined total dollar amount Josh earned this month is:
\[
\boxed{-4t + 1590}
\]