https://file.aiquickdraw.com/mathbot/file/1728415174503yi4wdm3j.jpg

Let's solve the problems shown in the image:

### 1a.
**Problem:** Determine the constant of proportionality that relates the amount of money earned, $ y $, to the number of hours, $ x $.

- Ashley earned $50 for 4 hours of babysitting.
- To find the constant of proportionality ($ k $), use the formula:
  \[
  k = \frac{y}{x}
  \]
  where $ y $ is the total earnings, and $ x $ is the number of hours.
  
- Plug in the values:
  \[
  k = \frac{50}{4} = 12.5
  \]

So, the constant of proportionality is **12.5**. This means Ashley earns $12.50 per hour.

---

### 1b.
**Problem:** Write an equation that represents $ y $, the amount of money earned for babysitting $ x $ hours.

- Using the constant of proportionality $ k = 12.5 $:
  \[
  y = 12.5x
  \]

This equation shows that Ashley earns $12.50 for every hour she babysits.

Would you like more details on this solution or have any further questions?

---

Here are 5 related questions to further your understanding:

1. If Ashley babysits for 6 hours, how much would she earn using the equation?
2. How many hours would Ashley need to babysit to earn $100?
3. What is the constant of proportionality if Ashley earns $60 for 5 hours of babysitting?
4. How would the equation change if Ashley earned $70 for 4 hours?
5. What does it mean when we say "constant of proportionality" in real-life scenarios?

**Tip:** When solving proportional relationships, always identify the constant by dividing the dependent variable by the independent variable (like earnings divided by hours).

Ashley earned $50 babysitting her neighbor’s children for 4 hours. Determine the constant of proportionality that relates the amount of money earned, y, to the number of hours, x. Write an equation that represents y, the amount of money earned for babysitting x hours.

In this problem, we determine the constant of proportionality for Ashley's babysitting job, where she earned $50 for 4 hours. This problem covers concepts like proportional relationships and writing linear equations. Suitable for Grade 7 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation