2. To make a certain colour of household paint, you need to mix \( \frac{3}{4} \ell \) of white paint with 15 ml of red paint and 10 ml of yellow paint. Express the paint mixture as a ratio. If you need a total volume of 31 litres of this paint, how much of each colour must you mix? 3. On Wednesday evening Sonto spent \( \frac{1}{2} \) hour doing homework, 45 minutes doing housework, 1 hour visiting friends and \( 1 \frac{1}{2} \) hours watching television. Write this information as a ratio. 4. In a country there are 48000 people in the defence services. They work in the army, navy and air force in the ratio \( 5: 2: 3 \). How many people are in each servic

Sure, let's tackle each of your questions step by step. --- ### **Question 2** **To make a certain colour of household paint, you need to mix** \( \frac{3}{4} \) **litres of white paint with 15 ml of red paint and 10 ml of yellow paint.** **a. Express the paint mixture as a ratio.** 1. **Convert All Measurements to the Same Unit:** - **White Paint:** \( \frac{3}{4} \) litres = **750 ml** (since 1 litre = 1000 ml) - **Red Paint:** **15 ml** - **Yellow Paint:** **10 ml** 2. **Write the Ratio:** \[ \text{White} : \text{Red} : \text{Yellow} = 750\ \text{ml} : 15\ \text{ml} : 10\ \text{ml} \] 3. **Simplify the Ratio:** - Find the greatest common divisor (GCD) of 750, 15, and 10, which is **5**. - Divide each part by 5: \[ \frac{750}{5} : \frac{15}{5} : \frac{10}{5} = 150 : 3 : 2 \] **Simplified Ratio:** **150 : 3 : 2** **b. If you need a total volume of 31 litres of this paint, how much of each colour must you mix?** 1. **Determine the Scaling Factor:** - **Initial Total Volume:** \[ 750\ \text{ml} + 15\ \text{ml} + 10\ \text{ml} = 775\ \text{ml} = 0.775\ \text{litres} \] - **Desired Total Volume:** **31 litres** - **Scaling Factor (SF):** \[ SF = \frac{31}{0.775} = 40 \] 2. **Calculate Each Component:** - **White Paint:** \[ 0.75\ \text{litres} \times 40 = 30\ \text{litres} \] - **Red Paint:** \[ 0.015\ \text{litres} \times 40 = 0.6\ \text{litres} = 600\ \text{ml} \] - **Yellow Paint:** \[ 0.01\ \text{litres} \times 40 = 0.4\ \text{litres} = 400\ \text{ml} \] **Final Mixture for 31 Litres:** - **30 litres of White Paint** - **0.6 litres (600 ml) of Red Paint** - **0.4 litres (400 ml) of Yellow Paint** --- ### **Question 3** **On Wednesday evening, Sonto spent:** - \( \frac{1}{2} \) hour doing **homework** - 45 minutes doing **housework** - 1 hour visiting **friends** - \( 1 \frac{1}{2} \) hours watching **television** **Write this information as a ratio.** 1. **Convert All Times to the Same Unit (Hours):** - **Homework:** \( \frac{1}{2} \) hour = **0.5 hours** - **Housework:** 45 minutes = **0.75 hours** - **Visiting Friends:** **1 hour** - **Watching Television:** \( 1 \frac{1}{2} \) hours = **1.5 hours** 2. **Write the Initial Ratio:** \[ \text{Homework} : \text{Housework} : \text{Visiting Friends} : \text{Television} = 0.5 : 0.75 : 1 : 1.5 \] 3. **Simplify the Ratio:** - To eliminate decimals, multiply each part by **4** (the smallest number that converts all to whole numbers): \[ 0.5 \times 4 : 0.75 \times 4 : 1 \times 4 : 1.5 \times 4 = 2 : 3 : 4 : 6 \] **Simplified Ratio:** **2 : 3 : 4 : 6** --- ### **Question 4** **In a country, there are 48,000 people in the defence services. They work in the army, navy, and air force in the ratio \( 5 : 2 : 3 \). How many people are in each service?** 1. **Understand the Ratio:** - **Army : Navy : Air Force = 5 : 2 : 3** 2. **Calculate Total Parts:** \[ 5 + 2 + 3 = 10\ \text{parts} \] 3. **Determine the Number of People per Part:** \[ \text{People per part} = \frac{48,000}{10} = 4,800 \] 4. **Calculate Each Service:** - **Army:** \[ 5 \times 4,800 = 24,000\ \text{people} \] - **Navy:** \[ 2 \times 4,800 = 9,600\ \text{people} \] - **Air Force:** \[ 3 \times 4,800 = 14,400\ \text{people} \] **Final Distribution:** - **Army:** 24,000 people - **Navy:** 9,600 people - **Air Force:** 14,400 people --- I hope these solutions help you understand how to approach each problem!