Write all ratios in their simplest form. 1. There are three children in the Skosana family. Each week the eldest earns R270, the middle child earns \( R 180 \) and the youngest earns R90. Express these amounts as a ratio. 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 service

Sure, let's tackle each problem step by step to express the ratios in their simplest forms and perform the necessary calculations. --- ### **Problem 1** **Earnings of the Skosana Family Children:** - **Eldest Child:** R270 - **Middle Child:** R180 - **Youngest Child:** R90 **Step 1: Express as a Ratio** The earnings can be expressed as: \[ 270 : 180 : 90 \] **Step 2: Simplify the Ratio** Find the greatest common divisor (GCD) of the numbers to simplify the ratio. - **GCD of 270, 180, and 90 is 90.** Divide each term by 90: \[ \frac{270}{90} : \frac{180}{90} : \frac{90}{90} = 3 : 2 : 1 \] **Simplified Ratio:** \[ 3 : 2 : 1 \] --- ### **Problem 2** **Paint Mixture Requirements:** - **White Paint:** \( \frac{3}{4} \) litre (750 millilitres) - **Red Paint:** 15 ml - **Yellow Paint:** 10 ml **Step 1: Convert All Measurements to the Same Unit** Convert litres to millilitres: \[ \frac{3}{4} \text{ litre} = 750 \text{ ml} \] **Step 2: Express as a Ratio** \[ 750 \text{ ml} : 15 \text{ ml} : 10 \text{ ml} \] **Step 3: Simplify the Ratio** Find the GCD of 750, 15, and 10, which is 5. Divide each term by 5: \[ \frac{750}{5} : \frac{15}{5} : \frac{10}{5} = 150 : 3 : 2 \] **Simplified Ratio:** \[ 150 : 3 : 2 \] **Step 4: Determine Amounts for 31 Litres Total Volume** Total parts in the ratio: \[ 150 + 3 + 2 = 155 \text{ parts} \] Calculate the value of each part: \[ \text{Total volume} = 31 \text{ litres} = 31,000 \text{ ml} \\ \text{Value of one part} = \frac{31,000}{155} = 200 \text{ ml per part} \] **Amounts to Mix:** \[ \text{White Paint} = 150 \times 200 = 30,000 \text{ ml} = 30 \text{ litres} \\ \text{Red Paint} = 3 \times 200 = 600 \text{ ml} \\ \text{Yellow Paint} = 2 \times 200 = 400 \text{ ml} \] --- ### **Problem 3** **Sonto's Activities on Wednesday Evening:** - **Homework:** \( \frac{1}{2} \) hour - **Housework:** 45 minutes - **Visiting Friends:** 1 hour - **Watching Television:** \( 1 \frac{1}{2} \) hours **Step 1: Convert All Times to the Same Unit (Minutes)** \[ \frac{1}{2} \text{ hour} = 30 \text{ minutes} \\ 45 \text{ minutes} = 45 \text{ minutes} \\ 1 \text{ hour} = 60 \text{ minutes} \\ 1 \frac{1}{2} \text{ hours} = 90 \text{ minutes} \] **Step 2: Express as a Ratio** \[ 30 : 45 : 60 : 90 \] **Step 3: Simplify the Ratio** Find the GCD of 30, 45, 60, and 90, which is 15. Divide each term by 15: \[ \frac{30}{15} : \frac{45}{15} : \frac{60}{15} : \frac{90}{15} = 2 : 3 : 4 : 6 \] **Simplified Ratio:** \[ 2 : 3 : 4 : 6 \] --- ### **Problem 4** **Distribution of People in Defence Services:** - **Total People:** 48,000 - **Ratio (Army : Navy : Air Force) = 5 : 2 : 3** **Step 1: Determine Total Parts in the Ratio** \[ 5 + 2 + 3 = 10 \text{ parts} \] **Step 2: Calculate the Number of People per Part** \[ \text{Each part} = \frac{48,000}{10} = 4,800 \text{ people} \] **Step 3: Calculate People in Each Service** \[ \text{Army} = 5 \times 4,800 = 24,000 \text{ people} \\ \text{Navy} = 2 \times 4,800 = 9,600 \text{ people} \\ \text{Air Force} = 3 \times 4,800 = 14,400 \text{ people} \] **Number of People in Each Service:** - **Army:** 24,000 - **Navy:** 9,600 - **Air Force:** 14,400 --- These solutions provide the simplest forms of the required ratios and perform the necessary calculations based on the given information.