Math Problem Statement

Leila works as a tutor for $9 an hour and as a waitress for $10 an hour. This month, she worked a combined total of hours 86 at her two jobs. Let be the number of hours Leila worked as a tutor this month. Write an expression for the combined total dollar amount she earned this month.

Solution

To find the total dollar amount Leila earned this month, let's break down her earnings from each job:

  • Let tt represent the number of hours Leila worked as a tutor.
  • Therefore, the number of hours she worked as a waitress will be 86t86 - t, since she worked a total of 86 hours combined at both jobs.

Tutor Earnings:

She earns $9 per hour as a tutor, so her earnings from tutoring are: 9t9t

Waitress Earnings:

She earns $10 per hour as a waitress, and she worked 86t86 - t hours as a waitress. So, her earnings from waitressing are: 10(86t)10(86 - t)

Combined Total Earnings:

The total amount Leila earned this month is the sum of her earnings from both jobs: Total Earnings=9t+10(86t)\text{Total Earnings} = 9t + 10(86 - t)

This expression represents the combined total dollar amount Leila earned this month.

Would you like a step-by-step simplification of this expression or further details on its components?


Here are some related questions:

  1. What is Leila's total earnings if she worked 40 hours as a tutor?
  2. How many hours must Leila work as a tutor to earn at least $500 from that job alone?
  3. If Leila worked 50 hours as a waitress, how much did she earn this month in total?
  4. How much will Leila earn if she only works as a tutor for all 86 hours?
  5. What is the maximum possible amount Leila could earn this month by working more hours as a waitress?

Tip: When solving word problems, clearly define variables and write out expressions step by step to avoid confusion.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations

Formulas

Total earnings = 9t + 10(86 - t)

Theorems

Distributive Property

Suitable Grade Level

Grades 6-8