3. Fill in the missing numbers to form equivalent rates. $$ \begin{array}{l} ext { a. } \frac{4 \mathrm{~L}}{10 \mathrm{~m}^{2}}=\frac{10 \mathrm{~L}}{5 \mathrm{~m}^{2}}=\frac{1}{\mathrm{~m}^{2}} \ ext { b. } \frac{\$ 9}{6 \mathrm{~min}}=\frac{}{2 \mathrm{~min}}=\frac{}{10 \mathrm{~min}}=\frac{-}{1 ext { hour }}\end{array} $$

Question

3. Fill in the missing numbers to form equivalent rates. $$ \begin{array}{l}	ext { a. } \frac{4 \mathrm{~L}}{10 \mathrm{~m}^{2}}=\frac{10 \mathrm{~L}}{5 \mathrm{~m}^{2}}=\frac{1}{\mathrm{~m}^{2}} \ 	ext { b. } \frac{\$ 9}{6 \mathrm{~min}}=\frac{}{2 \mathrm{~min}}=\frac{}{10 \mathrm{~min}}=\frac{-}{1 	ext { hour }}\end{array} $$

UpStudy AI · Accepted Answer

Sure, let's tackle both parts **a** and **b** of the problem by filling in the missing numbers to form equivalent rates.

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### **3. Fill in the missing numbers to form equivalent rates.**

#### **a.**

Given:
$$
\frac{4\, \text{L}}{10\, \text{m}^2} = \frac{10\, \text{L}}{5\, \text{m}^2} = \frac{1}{\text{m}^2}
$$

**Explanation:**

All parts of the equation represent the rate in terms of liters per square meter (L/m²). Each fraction simplifies to the same rate:

- $$\frac{4\, \text{L}}{10\, \text{m}^2} = \frac{2\, \text{L}}{5\, \text{m}^2}$$
- $$\frac{10\, \text{L}}{5\, \text{m}^2} = \frac{2\, \text{L}}{1\, \text{m}^2}$$
- $$\frac{1}{\text{m}^2}$$ is the simplified unit rate.

**Filled-In Equation:**
$$
\frac{4\, \text{L}}{10\, \text{m}^2} = \frac{10\, \text{L}}{5\, \text{m}^2} = \frac{2\, \text{L}}{1\, \text{m}^2}
$$

---

#### **b.**

Given:
$$
\frac{\$9}{6\, \text{min}} = \frac{\underline{\hspace{1cm}}}{2\, \text{min}} = \frac{\underline{\hspace{1cm}}}{10\, \text{min}} = \frac{\underline{\hspace{1cm}}}{1\, \text{hour}}
$$

**Objective:**
Fill in the blanks to represent equivalent rates in dollars for the given time intervals.

**Step-by-Step Solution:**

1. **Determine the Unit Rate:**
   $$
   \frac{\$9}{6\, \text{min}} = \frac{\$1.5}{1\, \text{min}}
   $$
   
2. **Calculate for 2 minutes:**
   $$
   \$1.5 \times 2 = \$3
   $$
   $$
   \frac{\$3}{2\, \text{min}}
   $$
   
3. **Calculate for 10 minutes:**
   $$
   \$1.5 \times 10 = \$15
   $$
   $$
   \frac{\$15}{10\, \text{min}}
   $$
   
4. **Calculate for 1 hour (60 minutes):**
   $$
   \$1.5 \times 60 = \$90
   $$
   $$
   \frac{\$90}{1\, \text{hour}}
   $$

**Filled-In Equation:**
$$
\frac{\$9}{6\, \text{min}} = \frac{\$3}{2\, \text{min}} = \frac{\$15}{10\, \text{min}} = \frac{\$90}{1\, \text{hour}}
$$

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### **Final Answer:**

**b.**
$$
\frac{\$9}{6\, \text{min}} = \frac{\$3}{2\, \text{min}} = \frac{\$15}{10\, \text{min}} = \frac{\$90}{1\, \text{hour}}
$$

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This ensures that all the rates are equivalent by maintaining the same ratio of dollars to time across different time intervals.
**a.** $$\frac{4\, \text{L}}{10\, \text{m}^2} = \frac{10\, \text{L}}{5\, \text{m}^2} = \frac{2\, \text{L}}{1\, \text{m}^2}$$ **b.** $$\frac{\$9}{6\, \text{min}} = \frac{\$3}{2\, \text{min}} = \frac{\$15}{10\, \text{min}} = \frac{\$90}{1\, \text{hour}}$$

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