4 chefs require 10 minutes to prepare 20 desserts. At this rate how many chefs are needed to prepare 75 desserts in 15 minutes

To solve this problem, we can use a proportional reasoning approach.

### Step 1: Determine the rate of dessert preparation.
First, let's find out the rate at which the chefs are preparing the desserts:

- **4 chefs prepare 20 desserts in 10 minutes.**

This means that in 1 minute, 4 chefs prepare:
\[
\frac{20 \text{ desserts}}{10 \text{ minutes}} = 2 \text{ desserts per minute}
\]

Therefore, the rate of dessert preparation per chef per minute is:
\[
\frac{2 \text{ desserts per minute}}{4 \text{ chefs}} = 0.5 \text{ desserts per chef per minute}
\]

### Step 2: Determine the total number of desserts needed in the given time.
We need to prepare 75 desserts in 15 minutes. The total number of desserts that need to be prepared per minute is:
\[
\frac{75 \text{ desserts}}{15 \text{ minutes}} = 5 \text{ desserts per minute}
\]

### Step 3: Calculate the number of chefs required.
We know that 1 chef can prepare 0.5 desserts per minute. To prepare 5 desserts per minute, the number of chefs required is:
\[
\frac{5 \text{ desserts per minute}}{0.5 \text{ desserts per chef per minute}} = 10 \text{ chefs}
\]

### Conclusion:
**10 chefs are needed to prepare 75 desserts in 15 minutes.**

Would you like further details or have any questions?

Here are 5 related questions:
1. How long would it take 6 chefs to prepare 100 desserts?
2. If one chef can prepare 1 dessert in 3 minutes, how many chefs are needed to prepare 60 desserts in 12 minutes?
3. How many desserts can 8 chefs prepare in 20 minutes?
4. If 5 chefs can prepare 30 desserts in 15 minutes, how many chefs are needed to prepare 60 desserts in 10 minutes?
5. How many minutes will it take for 12 chefs to prepare 120 desserts?

**Tip:** When working with rates, setting up a proportion can often simplify the calculation process.

Learn how to solve a rate problem involving chefs and desserts. Understand how to determine the number of chefs needed based on dessert preparation rates. Suitable for students in Grades 7-9.

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