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Let's go through the problems one by one:

### **Problem 11**
**Given:**
- The boiling point of water is 212°F.
- Formula for converting Fahrenheit to Celsius: $ C = \frac{5}{9}(F - 32) $
- You need to find the temperature in °C if the water is at 185°F.

**Solution:**
Use the given formula:
\[
C = \frac{5}{9}(185 - 32)
\]
Calculate:
\[
C = \frac{5}{9}(153) \approx 85.0^\circ C
\]
The closest answer is **85°C**.

### **Problem 12**
**Part A:**
- Total tickets sold = 72
- Ratio of adult to child tickets = 4:1

**Solution:**
Let $ x $ represent the number of child tickets. Then adult tickets would be $ 4x $.
So, $ x + 4x = 72 $
\[
5x = 72 \quad \Rightarrow \quad x = \frac{72}{5} = 14.4
\]
Thus, $ x = 14 $ child tickets (we round to the nearest whole number).
So, the number of adult tickets is $ 4 \times 14 = 56 $.

**Part B:**
The number of each type of ticket:
- Adult tickets: **56**
- Child tickets: **14**

### **Problem 13**
Use the given set of coordinates and identify the reflection across the x-axis.

- For each point, the reflection across the x-axis changes the sign of the y-coordinate while keeping the x-coordinate the same.
    - $ (2, 3) \rightarrow (2, -3) $
    - $ (-1, 0) \rightarrow (-1, 0) $
    - $ (4, -7) \rightarrow (4, 7) $

### **Problem 14**
**Part A:**
- Total spent by the club = $608
- 15 members
- Each food item costs $40 per hour.

**Solution:**
Let $ x $ be the number of hours.
\[
40x \times 15 = 608
\]
Solve for $ x $:
\[
600x = 608 \quad \Rightarrow \quad x = \frac{608}{600} = 1.0133 \approx 1 \text{ hour}
\]

**Part B:**
Amount spent on food:
\[
\text{Total} = 15 \times 40 \times 1 = \$600
\]

### **Problem 15**
**Finding common factors of 63 and 72:**
- Prime factors of 63: $ 63 = 3^2 \times 7 $
- Prime factors of 72: $ 72 = 2^3 \times 3^2 $

**Greatest common factor:** $ 3^2 = 9 $

Do you need more details or have any questions? Here are five related questions to expand your understanding:

1. How do you derive the formula to convert temperatures between Celsius and Fahrenheit?
2. What is the process for determining the number of tickets sold given a different ratio?
3. How do you determine the reflection of a point over the y-axis instead of the x-axis?
4. How would the calculations change in Problem 14 if the number of members was different?
5. What other methods can you use to find the greatest common factor of two numbers?

**Tip:** When solving word problems, breaking them down into smaller parts can help clarify the steps needed to find the solution.

The boiling point of water is 212°F. In degrees Celsius, how much do I have to add to boil water that is already 185°F? Use the formula C = 5/9 * (F-32) where C represents the temperature in degrees Celsius and F represents the temperature in degrees Fahrenheit.  A small theater sold 72 tickets for a play. The ratio of adult tickets to child tickets was 4:1. The ratio of adult tickets to senior tickets was 4:1. Use the given set of coordinates to write the reflection across the x-axis of each point on the left. The drama club spent $608 on food for the party for its 15 members. The bill for each food item was $40 per hour. Draw a Venn diagram to show the common factors of 63 and 72, then circle the greatest common factor.

Solve temperature conversion from Fahrenheit to Celsius, calculate ticket sales based on ratios, understand reflection across the x-axis, and find the greatest common factor with Venn diagrams. Detailed step-by-step solutions for Grades 6-8.

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