A positive two-digit number is such that the product of the digits is 20. When the digits are reversed, the number so formed is greater than the original number by 9. Find the number.

You're on a roll — Here is the solution to the number problem: 6. A positive two-digit number is such that the product of the digits is 20. When the digits are reversed, the number so formed is greater than the original number by 9. Find the number. (3 marks) Step 1: Represent the two-digit number using variables. Let the tens digit be t and the units digit be u. The original number can be expressed as 10t + u. The reversed number can be expressed as 10u + t. Step 2: Formulate equations based on the given conditions. Condition 1: The product of the digits is 20. t × u = 20 (1) Condition 2: When the digits are reversed, the new number is greater than the original number by 9. 10u + t = (10t + u) + 9 (2) Step 3: Simplify Equation (2). 10u + t = 10t + u + 9 Subtract u and t from both sides: 9u - 9t = 9 Divide by 9: u - t = 1 u = t + 1 (3) Step 4: Substitute Equation (3) into Equation (1). Substitute u = t + 1 into t × u = 20: t(t + 1) = 20 t^2 + t = 20 Rearrange into a quadratic equation: t^2 + t - 20 = 0 Step 5: Solve the quadratic equation for t. Factor the quadratic equation: (t + 5)(t - 4) = 0 This gives two possible values for t: t = -5 or t = 4 Since t is a digit of a positive two-digit number, it must be a positive integer between 1 and 9. Therefore, t = 4. Step 6: Find the value of u. Using Equation (3), u = t + 1: u = 4 + 1 u = 5 Step 7: State the original number. The tens digit is t=4 and the units digit is u=5. The original number is 10t + u = 10(4) + 5 = 40 + 5 = 45. Check the conditions: Product of digits: 4 × 5 = 20 (Correct) Reversed number: 54. Original number: 45. Is 54 = 45 + 9? Yes, 54 = 54 (Correct) The number is 45. Drop the next question.