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Let's solve the two parts of the problem step by step:

### Given Ingredients for 6 People:
- 800 g pineapple
- 4 egg whites
- ½ lemon
- 100 g caster sugar

### a) Ann makes pineapple sorbet for 9 people. Work out how much pineapple she uses.

We know the original recipe is for 6 people and uses 800 g of pineapple. To find how much pineapple Ann will use for 9 people, we can set up a proportion:

\[
\frac{800 \, \text{g}}{6 \, \text{people}} = \frac{x \, \text{g}}{9 \, \text{people}}
\]

Cross-multiply to solve for \( x \):

\[
x = \frac{800 \times 9}{6} = 1200 \, \text{g}
\]

So, Ann uses **1200 g** of pineapple.

---

### b) Dan makes pineapple sorbet. He uses 2½ lemons. Work out how many people he makes pineapple sorbet for.

The original recipe uses ½ lemon for 6 people. Dan uses 2½ lemons, so we set up another proportion to find how many people this amount serves:

\[
\frac{0.5 \, \text{lemon}}{6 \, \text{people}} = \frac{2.5 \, \text{lemons}}{y \, \text{people}}
\]

Cross-multiply to solve for \( y \):

\[
y = \frac{2.5 \times 6}{0.5} = 30 \, \text{people}
\]

So, Dan makes sorbet for **30 people**.

---

Would you like further details on any of the steps? Here are five related questions:

1. How would the amount of caster sugar change if Ann made sorbet for 12 people?
2. What would happen if Dan only had 1 lemon? How many people could he serve?
3. If the recipe used 1 lemon for 6 people, how many lemons would Dan need for 30 people?
4. How much pineapple would Dan need if he served 30 people?
5. What is the ratio of pineapple to egg whites in the original recipe?

**Tip:** Proportions are a great way to scale recipes up or down.

Here are the ingredients for making pineapple sorbet for 6 people: 800 g pineapple, 4 egg whites, ½ lemon, 100 g caster sugar. a) Ann makes pineapple sorbet for 9 people. Work out how much pineapple she uses. b) Dan makes pineapple sorbet. He uses 2½ lemons. Work out how many people he makes pineapple sorbet for.

Solve a pineapple sorbet recipe problem using ratios and proportions. Calculate the amount of pineapple Ann needs for 9 people and find out how many people Dan can serve with 2½ lemons. This math problem is suitable for Grades 7-9, focusing on proportional reasoning.

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