(B) Read and answer the following questions: i. I think of a number. I multiply it by 5 . I then subtract 19 . Finally, I double the result. The final answer is 22 . What number did I think of? ( 6 Marks) ii. I subtract 15 from a certain number and divide the result by 3. The result is the same as adding 4 to the number and then dividing by 5 . Find the number. ( 6 Marks)

Let's solve each part step by step. ### Part (i) 1. **Define the variable**: Let the number I think of be \( x \). 2. **Translate the operations into an equation**: - I multiply it by 5: \( 5x \) - I then subtract 19: \( 5x - 19 \) - Finally, I double the result: \( 2(5x - 19) \) - The final answer is 22: \[ 2(5x - 19) = 22 \] 3. **Solve the equation**: - First, distribute the 2: \[ 10x - 38 = 22 \] - Next, add 38 to both sides: \[ 10x = 60 \] - Finally, divide by 10: \[ x = 6 \] So, the number I thought of is \( 6 \). ### Part (ii) 1. **Define the variable**: Let the certain number be \( y \). 2. **Translate the operations into an equation**: - I subtract 15 from the number: \( y - 15 \) - I divide the result by 3: \[ \frac{y - 15}{3} \] - The result is the same as adding 4 to the number and then dividing by 5: \[ \frac{y + 4}{5} \] - Therefore, we can set up the equation: \[ \frac{y - 15}{3} = \frac{y + 4}{5} \] 3. **Solve the equation**: - Cross-multiply to eliminate the fractions: \[ 5(y - 15) = 3(y + 4) \] - Distribute both sides: \[ 5y - 75 = 3y + 12 \] - Subtract \( 3y \) from both sides: \[ 2y - 75 = 12 \] - Add 75 to both sides: \[ 2y = 87 \] - Finally, divide by 2: \[ y = 43.5 \] So, the certain number is \( 43.5 \). ### Summary of Answers: - Part (i): The number I thought of is \( 6 \). - Part (ii): The certain number is \( 43.5 \).