Peyton is a waitress at a restaurant. Each day she works, Peyton will make a guaranteed wage of $30, however the additional amount that Peyton earns from tips depends on the number of tables she waits on that day. From past experience, Peyton noticed that she will get about $9 in tips for each table she waits on. How much would Peyton expect to earn in a day on which she waits on 16 tables? How much would Peyton expect to make in a day when waiting on t*t* tables?

To calculate how much Peyton would expect to earn in a day, we can set up a linear expression based on the information provided.

### 1. Peyton's Earnings with 16 Tables
Peyton's total earnings for the day can be calculated using the formula:

\[
\text{Total earnings} = \text{Guaranteed wage} + (\text{Tip per table} \times \text{Number of tables})
\]

Given:
- Guaranteed wage = $30
- Tip per table = $9
- Number of tables = 16

Substitute the values into the formula:

\[
\text{Total earnings} = 30 + (9 \times 16) = 30 + 144 = 174
\]

So, Peyton would expect to earn $174 in a day when she waits on 16 tables.

### 2. Peyton's Earnings with $ t \times t $ Tables
If Peyton waits on $ t \times t $ tables in a day, we use the same formula:

\[
\text{Total earnings} = 30 + (9 \times t^2)
\]

Here, $ t \times t = t^2 $, so the expression becomes:

\[
\text{Total earnings} = 30 + 9t^2
\]

This represents how much Peyton would expect to earn in a day when she waits on $ t \times t $ tables.

Would you like more details or have any questions? Here are five related questions to explore further:

1. What would Peyton's earnings be if she waited on 10 tables in a day?
2. How would her earnings change if the tips per table increased to $12?
3. What is the minimum number of tables Peyton needs to wait on to earn at least $100 in a day?
4. How does the expression for Peyton's total earnings change if the guaranteed wage increases to $50?
5. How would you represent Peyton's earnings if the tip amount per table was a variable instead of a fixed $9?

**Tip:** When working with problems involving rates or earnings, it's useful to set up a formula that relates the variables, as this can easily be adjusted for different scenarios.

Learn how to calculate Peyton's earnings when she waits on 16 tables. Understand the formula for total earnings including guaranteed wage and tips per table. Suitable for middle school students and those interested in practical math problems.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation