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We are given:

- Blue and yellow dyes are mixed in an **8:3** ratio to make **44 litres** of green-coloured dye.
- **8 litres** of yellow dye are then added.

We need to determine the new ratio of blue to yellow dye in its simplest form.

### Step 1: Find the original amounts of blue and yellow dye

Since the dyes are mixed in an 8:3 ratio and the total volume is 44 litres, we can calculate how much of each dye is used.

- The total number of parts = \( 8 + 3 = 11 \) parts.
- Each part represents \( \frac{44}{11} = 4 \) litres.

Thus:
- Blue dye = \( 8 \times 4 = 32 \) litres.
- Yellow dye = \( 3 \times 4 = 12 \) litres.

### Step 2: Add the extra 8 litres of yellow dye

After adding 8 litres of yellow dye, the total amount of yellow dye becomes:
- \( 12 + 8 = 20 \) litres of yellow dye.

### Step 3: Find the new ratio

Now, we compare the amounts of blue dye (which remains 32 litres) and yellow dye (now 20 litres).

The new ratio of blue to yellow dye is:
\[
\frac{32}{20} = \frac{8}{5}
\]

So, the new ratio of blue to yellow dye in its simplest form is **8:5**.

Would you like more details or have any further questions?

Here are some related questions you might consider:
1. How would the ratio change if you added more blue dye instead of yellow?
2. If 60 litres of dye were produced instead of 44 litres, how would the original ratio affect the amounts of blue and yellow?
3. What would happen if equal amounts of blue and yellow dye were added to the mixture?
4. How do you simplify ratios, and why is it important?
5. If another dye was added to the mixture, how would that impact the ratios?

**Tip:** When working with ratios, always ensure to simplify them to their lowest terms by dividing both numbers by their greatest common divisor.

Blue and yellow dye are mixed in an 8:3 ratio to make 44 litres of a green-coloured dye. A further 8 litres of yellow dye are added to the mixture. What is the new ratio of blue to yellow dye in its simplest form?

Learn how to find the new ratio of blue to yellow dye when 8 litres of yellow dye are added to an existing 8:3 ratio. This problem involves simplifying the final ratio, making it suitable for students in Grades 6-8. The total volume of dye is 44 litres, and the new ratio of blue to yellow dye is calculated step-by-step.

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