This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here are the answers to your questions: 6. To find the two-digit number: Step 1: Define the number using variables. Let the two-digit number be 10t + u, where t is the tens digit and u is the units digit. Step 2: Formulate equations based on the given conditions. Condition 1: The product of its digits is 20. t × u = 20 (1) Condition 2: When the digits are reversed, the number formed is greater than the original number by 9. The reversed number is 10u + t. 10u + t = (10t + u) + 9 10u + t = 10t + u + 9 9u - 9t = 9 Divide by 9: u - t = 1 (2) Step 3: Solve the system of equations. From equation (2), express u in terms of t: u = t + 1 Substitute this into equation (1): t(t + 1) = 20 t^2 + t = 20 t^2 + t - 20 = 0 Step 4: 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 must be a positive digit, we take t = 4. Step 5: Find the value of u. Using u = t + 1: u = 4 + 1 = 5 Step 6: Form the original number. The number is 10t + u = 10(4) + 5 = 45. Check: Product of digits 4 × 5 = 20. Reversed number is $