the ratio of boys to girls in a school is \( 4: 6 \) and there are 1200 learners. 3.1 How many girls are there? 3.4. How many boys are there?

To solve the problem, we first need to understand the ratio of boys to girls, which is given as \( 4:6 \). This can be simplified to \( 2:3 \) by dividing both parts of the ratio by 2. Next, we can denote the number of boys as \( 2x \) and the number of girls as \( 3x \), where \( x \) is a common multiplier. Given that the total number of learners (boys + girls) is 1200, we can set up the equation: \[ 2x + 3x = 1200 \] Now, let's solve for \( x \): \[ 5x = 1200 \] Dividing both sides by 5: \[ x = \frac{1200}{5} = 240 \] Now that we have \( x \), we can find the number of girls and boys: 1. **Number of girls**: \[ \text{Girls} = 3x = 3 \times 240 = 720 \] 2. **Number of boys**: \[ \text{Boys} = 2x = 2 \times 240 = 480 \] Thus, the answers are: - **3.1**: There are 720 girls. - **3.4**: There are 480 boys.