https://file.aiquickdraw.com/mathbot/file/1726451060314kmg1vini.jpg

The problem in the image asks the following:

"A recipe that serves 8 people requires \( 1 \frac{1}{4} \) cups of sugar. Using this recipe, how many cups of sugar are needed to serve 24 people?"

### Let's break it down:
- The recipe serves 8 people with \( 1 \frac{1}{4} \) cups of sugar.
- We need to find out how much sugar is needed to serve 24 people.

### Step 1: Convert the mixed fraction to an improper fraction.
\[
1 \frac{1}{4} = \frac{5}{4} \text{ cups of sugar}
\]

### Step 2: Determine the number of cups of sugar per person.
For 8 people, \( \frac{5}{4} \) cups of sugar are used. So, for 1 person, the amount of sugar would be:
\[
\text{Sugar per person} = \frac{5}{4} \div 8 = \frac{5}{4} \times \frac{1}{8} = \frac{5}{32} \text{ cups of sugar per person}
\]

### Step 3: Calculate the sugar needed for 24 people.
To find the amount of sugar for 24 people, multiply the sugar per person by 24:
\[
\text{Sugar for 24 people} = \frac{5}{32} \times 24 = \frac{120}{32} = \frac{15}{4} = 3 \frac{3}{4} \text{ cups of sugar}
\]

### Final Answer:
\[
3 \frac{3}{4} \text{ cups of sugar are needed to serve 24 people.}
\]

Let me know if you'd like further explanation or details.

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Here are five related questions for practice:
1. How many cups of sugar are needed for 16 people?
2. If the recipe required 2 cups of sugar for 8 people, how much would be needed for 24 people?
3. If you only want to serve 4 people, how much sugar would you need?
4. How many people can be served with \( \frac{15}{4} \) cups of sugar?
5. If you doubled the sugar required for the original recipe, how much would be needed for 24 people?

**Tip:** When scaling a recipe, always find the amount per person and then multiply by the number of people you need to serve.

A recipe that serves 8 people requires 1 1/4 cups of sugar. Using this recipe, how many cups of sugar are needed to serve 24 people?

Learn how to calculate the amount of sugar needed for 24 people based on a recipe for 8. This example uses proportional scaling and fraction operations. Suitable for middle school students.

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