https://file.aiquickdraw.com/mathbot/file/1727363792193n2a6mrbo.jpg

To solve this problem, we need to determine the total prize based on how the winnings are distributed according to the contributions of Jim, John, and Mike.

### Step-by-Step Solution:

1. **Contribution Ratios**:  
   - Jim's contribution: 36  
   - John's contribution: 30  
   - Mike's contribution: 24  
   
   The ratio of contributions is \(36:30:24\). We can simplify this ratio by dividing all values by their greatest common divisor (GCD), which is 6:  
   \[
   36 \div 6 = 6, \quad 30 \div 6 = 5, \quad 24 \div 6 = 4
   \]
   So, the simplified ratio is \(6:5:4\).

2. **Mike's Share of the Prize**:  
   We know that Mike's share of the prize is R5,400. Mike's share corresponds to the "4" part of the ratio \(6:5:4\).

3. **Total Parts in the Ratio**:  
   The total parts in the ratio are:  
   \[
   6 + 5 + 4 = 15
   \]
   So, the entire prize is divided into 15 parts.

4. **Determine the Value of Each Part**:  
   Since Mike's 4 parts are worth R5,400, the value of 1 part is:  
   \[
   \frac{5,400}{4} = 1,350
   \]

5. **Calculate the Total Prize**:  
   Since the total prize is made up of 15 parts, and each part is worth R1,350, the total prize is:  
   \[
   15 \times 1,350 = 20,250
   \]

### Final Answer:
The total prize is **20,250**.

Would you like more details or have any questions? 

Here are some related questions:
1. What is the method for simplifying ratios like \(36:30:24\)?
2. How can we find the GCD of multiple numbers to simplify ratios?
3. What if John’s contribution was increased? How would that affect the prize distribution?
4. Can this type of ratio problem be solved using a formula for direct proportionality?
5. How would the solution change if the prize was divided by a different method?

**Tip:** Simplifying ratios is key to solving problems involving proportional distribution efficiently.

Prize money is to be shared between three friends according to the ratio of their contributions to the ticket. Jim contributed R36, John contributed R30, and Mike contributed R24. Mike's share of the winnings is R5,400. What was the total amount of the prize?

Solve a prize distribution problem where contributions of R36, R30, and R24 result in a ratio. Mike's share is R5,400, and this step-by-step solution shows how to calculate the total prize based on ratio and proportions. Suitable for Grades 6-8.

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