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Let me extract and solve the math problems shown in the image.The image shows a math worksheet with several problems involving ratios and proportional reasoning. I'll break down and solve each problem.

### Problem 1:
**Question**: "Evaluate each ratio. Compare the quantities using a ratio."
- The numbers in the boxes appear to be 12 and 15.

**Solution**:
The ratio of 12 to 15 is \( \frac{12}{15} \). Simplifying this:
\[
\frac{12}{15} = \frac{4}{5}
\]
The simplified ratio is \( 4:5 \).

---

### Problem 2:
**Question**: "Rachel is making trail mix. She mixes 5 cups of raisins with 10 cups of peanuts. Complete the ratio table."

The table includes a ratio of raisins to peanuts, and the first row shows 5 cups of raisins to 10 cups of peanuts.

**Solution**:
The ratio is 5:10, which simplifies to 1:2 (1 cup of raisins for every 2 cups of peanuts).

We can complete the ratio table by multiplying or dividing the original ratio:
- 1 cup of raisins = 2 cups of peanuts
- 2 cups of raisins = 4 cups of peanuts
- 3 cups of raisins = 6 cups of peanuts
- 4 cups of raisins = 8 cups of peanuts
- 5 cups of raisins = 10 cups of peanuts

---

### Problem 3:
**Question**: "Rachel is making fruit punch. The recipe calls for 3 cups of canned peaches to 2 cups of orange juice. Complete the ratio table."

The table starts with 3 cups of peaches and 2 cups of orange juice.

**Solution**:
The ratio is 3:2 (3 cups of peaches for every 2 cups of orange juice).

To complete the ratio table:
- 3 cups of peaches = 2 cups of orange juice
- 6 cups of peaches = 4 cups of orange juice
- 9 cups of peaches = 6 cups of orange juice
- 12 cups of peaches = 8 cups of orange juice

---

### Problem 4:
**Question**: "Tina is stuffing envelopes. She stuffs 50 envelopes in 30 minutes. Complete the ratio table."

The table starts with 0.5 envelopes and scales up to 2 envelopes.

**Solution**:
Tina stuffs 50 envelopes in 30 minutes, so her rate is:
\[
\text{Rate} = \frac{50}{30} = \frac{5}{3} \text{ envelopes per minute}.
\]
Now, we'll calculate the time for different numbers of envelopes:
- 0.25 envelopes: \( \frac{0.25}{\frac{5}{3}} = 0.15 \) minutes
- 0.5 envelopes: \( \frac{0.5}{\frac{5}{3}} = 0.3 \) minutes
- 1 envelope: \( \frac{1}{\frac{5}{3}} = 0.6 \) minutes
- 2 envelopes: \( \frac{2}{\frac{5}{3}} = 1.2 \) minutes

---

Would you like a deeper explanation of any of these problems? Here are five related questions for further practice:

1. If Rachel uses 15 cups of raisins, how many cups of peanuts does she need?
2. How much time would Tina need to stuff 100 envelopes?
3. What is the ratio of 24 to 36 in simplest form?
4. How many cups of orange juice are needed if Rachel uses 18 cups of canned peaches?
5. If Tina increases her speed and stuffs 75 envelopes in 30 minutes, what is her new rate?

**Tip**: When working with ratios, always check if you can simplify the terms to make calculations easier.

Evaluate the ratios and complete the tables involving raisins, peanuts, fruit punch ingredients, and the rate of stuffing envelopes.

This page provides a detailed explanation of ratios, including how to simplify them and apply them to real-world problems like mixing trail mix, fruit punch, and calculating work rates. Suitable for students in Grades 6-8.

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