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Let's break down the problem step by step.

### Information given:
- 3 lions eat as much as 4 leopards.
- 5 bears eat as much as 9 leopards.
- The zoo has enough food for **9 lions and 14 leopards for 30 days**.
- We are asked how many days the same food will last for **12 lions, 10 bears, and 5 leopards**.

### Step 1: Convert lions and bears into leopards for easier calculation.

1. **Lions to leopards**:
   - 3 lions = 4 leopards.
   - Therefore, 1 lion = \( \frac{4}{3} \) leopards.

2. **Bears to leopards**:
   - 5 bears = 9 leopards.
   - Therefore, 1 bear = \( \frac{9}{5} \) leopards.

### Step 2: Calculate the total equivalent leopards for the initial food supply.
- The food supply is for **9 lions and 14 leopards for 30 days**.
- Convert the 9 lions into leopards:
  \[
  9 \text{ lions} = 9 \times \frac{4}{3} = 12 \text{ leopards}.
  \]
- So, the total equivalent leopards the food can support is:
  \[
  12 \text{ leopards (from lions)} + 14 \text{ leopards} = 26 \text{ leopards}.
  \]
- This food lasts for **30 days**, so the food supply is enough for:
  \[
  26 \text{ leopards for 30 days}.
  \]

### Step 3: Calculate the total leopards for the new set of animals.
We need to find out how many equivalent leopards there are for **12 lions, 10 bears, and 5 leopards**.

1. Convert **12 lions** to leopards:
   \[
   12 \text{ lions} = 12 \times \frac{4}{3} = 16 \text{ leopards}.
   \]
2. Convert **10 bears** to leopards:
   \[
   10 \text{ bears} = 10 \times \frac{9}{5} = 18 \text{ leopards}.
   \]
3. Add the **5 leopards**:
   \[
   \text{Total leopards} = 16 \text{ (from lions)} + 18 \text{ (from bears)} + 5 \text{ (leopards)} = 39 \text{ leopards}.
   \]

### Step 4: Calculate how long the food will last.
The food supply supports **26 leopards for 30 days**. Now we have 39 leopards, so the number of days the food will last is:
\[
\text{Days} = \frac{26}{39} \times 30 = \frac{2}{3} \times 30 = 20 \text{ days}.
\]

### Final Answer:
The food will last for **20 days**.

Would you like a detailed explanation of any step, or do you have any questions? Here are some related questions to explore:

1. What if the zoo had 15 lions instead of 12? How would that change the calculation?
2. How would the answer change if the zoo had fewer bears?
3. Can you generalize a formula for calculating how long the food lasts for any number of lions, bears, and leopards?
4. If the food only lasted 25 days for the original supply, how many days would it last with 12 lions, 10 bears, and 5 leopards?
5. How would the total number of days change if 1 lion ate as much as 5 leopards?

Tip: Always express everything in terms of a common unit (e.g., leopards) for easier calculations.

In a zoo, 3 lions eat as much food as 4 leopards, while 5 bears eat as much as 9 leopards. If they have enough food for 9 lions and 14 leopards for 30 days, how many days will this food last if there are 12 lions, 10 bears, and 5 leopards?

Solve the problem of how long food lasts in a zoo for 12 lions, 10 bears, and 5 leopards based on their eating proportions with detailed steps. Learn how to convert between animals using their food consumption ratios. Suitable for students in Grades 9-11.

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