https://file.aiquickdraw.com/mathbot/file/17260712561336yizm0v2.jpg

Let's solve the problem step by step.

### Step 1: Initial Dye Calculation
The dyes are mixed in a ratio of 9:2, which means for every 9 parts of yellow dye, there are 2 parts of red dye.

Given:
- The total mixture is 44 liters.

Let the amount of yellow dye be \( 9x \) and the amount of red dye be \( 2x \). So:

\[
9x + 2x = 44
\]

\[
11x = 44
\]

\[
x = 4
\]

So:
- Yellow dye = \( 9 \times 4 = 36 \) liters
- Red dye = \( 2 \times 4 = 8 \) liters

### Step 2: Adding More Red Dye
An additional 8 liters of red dye is added to the mixture.

New amount of red dye:
\[
8 + 8 = 16 \text{ liters}
\]

### Step 3: New Ratio of Yellow to Red Dye
The new ratio of yellow to red dye is:

\[
\text{Yellow} : \text{Red} = 36 : 16
\]

Simplify this ratio by dividing both sides by their greatest common divisor, which is 4:

\[
\frac{36}{4} : \frac{16}{4} = 9 : 4
\]

### Final Answer:
The new ratio of yellow to red dye is **9:4**.

Would you like more details or have any questions?

---

Here are five related questions you might find interesting:
1. What would the new ratio be if instead of 8 liters, 12 liters of red dye were added?
2. How would the total volume change if 10 liters of yellow dye were added instead of red dye?
3. If the original mixture had 20 liters of red dye, what would the new ratio be after adding 8 liters of red dye?
4. How would you calculate the amount of yellow dye needed to maintain the original 9:2 ratio after the red dye increase?
5. What would the impact on the color shade be if different amounts of dye are added?

**Tip:** Simplifying ratios often involves finding the greatest common divisor (GCD) to reduce the terms to their smallest whole numbers.

Yellow and red dye are mixed in a 9:2 ratio to make 44 litres of an orange-coloured dye. A further 8 litres of red dye are added to the mixture. What is the new ratio of yellow to red dye in its simplest form?

Learn how to solve a ratio problem involving the mixing of yellow and red dyes in a 9:2 ratio. The problem involves adding 8 litres of red dye and calculating the new simplified ratio, with step-by-step guidance. Suitable for Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation