https://file.aiquickdraw.com/mathbot/file/1727057950437r6l25k4l.jpg

To find the proportional equation that expresses earnings $ e $ in terms of hours worked $ h $, we can first determine the hourly rate using the given data.

The table provides three data points:

- 13 hours → \$387.40
- 17 hours → \$506.60
- 30 hours → \$894

### Step 1: Find the hourly rate of pay
Since the earnings appear to be proportional to the hours worked, we can find the hourly rate by dividing the earnings by the hours worked. Let's calculate the hourly rate using all three data points to ensure consistency.

#### For 13 hours:
\[
\text{Hourly rate} = \frac{387.40}{13} = 29.8
\]

#### For 17 hours:
\[
\text{Hourly rate} = \frac{506.60}{17} = 29.8
\]

#### For 30 hours:
\[
\text{Hourly rate} = \frac{894}{30} = 29.8
\]

Since the hourly rate is the same across all three data points, it confirms the relationship is proportional. The hourly rate is $ 29.8 $ dollars per hour.

### Step 2: Write the equation
The equation for earnings $ e $ in terms of hours worked $ h $ is:
\[
e = 29.8h
\]

This equation represents the proportional relationship between Andres's earnings and the hours he works.

Let me know if you would like more details or have any questions! Here are some related questions:

1. How would you calculate total earnings if Andres worked 40 hours?
2. What is the proportional constant in the equation?
3. How can you verify if a relationship is proportional given a set of values?
4. Can you express the number of hours worked $ h $ in terms of earnings $ e $?
5. If Andres's hourly rate increased to \$32 per hour, how would the equation change?

**Tip:** Always verify the consistency of the rate when dealing with proportional relationships by checking multiple points in the dataset.

If e represents his total earnings in dollars and cents for any number of hours worked, h, write a proportional equation for e in terms of h that matches the context. The data provided includes hours worked and corresponding earnings.

Learn how to derive a proportional equation for earnings based on hours worked using a dataset. This problem demonstrates key algebraic concepts like proportional relationships and linear equations, suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation