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.