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).
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Tutoring Earnings: Josh earns $11 for each hour he works as a tutor. If he worked \( t \) hours, his earnings from tutoring would be: \[ 11t \]
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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: \[ 15(106 - t) \]
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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: \[ \boxed{-4t + 1590} \]