Archie made some cupcakes for a charity coffee morning. The ratio of chocolate cupcakes to strawberry cupcakes was 3:1 The ratio of strawberry cupcakes to lemon cupcakes was 2:3 (a) Write down the ratio of chocolate to strawberry to lemon cupcakes. (b) Work out the smallest possible number of cupcakes that Archie could have made.

Let's solve the problem step by step.

### Part (a) Write down the ratio of chocolate to strawberry to lemon cupcakes.

Given ratios:
- Chocolate : Strawberry = 3 : 1
- Strawberry : Lemon = 2 : 3

First, we need to express these ratios in terms of all three types of cupcakes.

1. The ratio of Chocolate : Strawberry is given as 3:1.
2. The ratio of Strawberry : Lemon is given as 2:3.

Since Strawberry is the common part in both ratios, we'll adjust them to match.

- From Chocolate : Strawberry = 3 : 1, we can write this as Chocolate : Strawberry = 3 : 1.
- From Strawberry : Lemon = 2 : 3, we want to match the Strawberry part to the 1 part in the first ratio.

To do this, we'll multiply the first ratio (Chocolate : Strawberry) by 2, so that the Strawberry part matches the second ratio:

\[
\text{Chocolate : Strawberry = 3(2) : 1(2) = 6 : 2}
\]
\[
\text{Strawberry : Lemon = 2 : 3}
\]

Now, we can combine these ratios:

- Chocolate : Strawberry : Lemon = 6 : 2 : 3.

So, the ratio of Chocolate to Strawberry to Lemon cupcakes is **6:2:3**.

### Part (b) Work out the smallest possible number of cupcakes that Archie could have made.

To find the smallest possible number of cupcakes, we add the parts of the ratio:

\[
\text{Total parts} = 6 (\text{Chocolate}) + 2 (\text{Strawberry}) + 3 (\text{Lemon}) = 11 \text{ parts}.
\]

Since the ratio is in whole numbers, the smallest possible number of cupcakes that Archie could have made is the sum of these parts:

\[
\text{Smallest possible number of cupcakes} = 11.
\]

So, **11** is the smallest possible number of cupcakes that Archie could have made.

Would you like further details or have any questions?

Here are 5 related questions for further practice:

1. If Archie made 33 chocolate cupcakes, how many lemon cupcakes did he make?
2. If the total number of cupcakes is 66, how many of them are strawberry?
3. If 10 more chocolate cupcakes are added, what will be the new ratio of chocolate to strawberry to lemon?
4. If the ratio of lemon to strawberry cupcakes changes to 4:2, what will be the new ratio of chocolate to strawberry to lemon?
5. If 5 strawberry cupcakes are removed, what is the new ratio of chocolate to strawberry to lemon?

**Tip:** When solving ratio problems involving three quantities, always align them based on the common term, and adjust the ratios accordingly before combining them.

Learn how to solve a ratio problem involving chocolate, strawberry, and lemon cupcakes with a detailed step-by-step solution. This problem covers ratio and proportion concepts, suitable for students in Grades 6-8.

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