
Digit problems are problems involving numbers with two or more digits. Example: 89 8 tens or 8 x 10 = 80 9 units or 9 x 1 = 9 Sum = 89 The number is expressed as 10t + u, where t is the digit in the tens place and u is the digit in the units place. Example: 456 4 one hundreds or 4 x 100 = 400 5 tens or 5 x 10 = 50 6 units or 6 x 1 = 6 Sum = 456 The number is expressed as 100h + 10t + u, where h is the digit in the hundreds place and t is the digit in the tens place and u is the digit in the units place. Method 1: Example: The sum of the digits of a twodigit number is 4. The ones digit is three times the tens digit. What is the number? Solution: Let 'u' be the digit in the units place and 't' be the digit in the tens place. t + u = 4 u = 3t substituting u = 3t in t + u = 4 t + u = 4 t + 3t = 4 4t = 4 t = 1 u = 3t = 3x1 = 3 The number is 13 Example: The sum of the digits of a two digit number is 7. When the digits are reversed, the number is increased by 27. Find the number? Solution: Let 'u' be the number in the units place and 't' be the number in the tens place. The algebraic equations can be written: The sum of the digits of a two digit number is 7 as t + u = 7 The digits are reversed can be written as 10u + t. When the digits are reversed, the number is increased by 27 can be written as 10u + t = 10t + u + 27. Solving for t and u: t + u = 7 t = 7  u 10u + t = 10t + u + 27 10u + 7  u = 10(7  u) + u + 27 10u + 7  u = 70  10u + u + 27 9u + 7 = 9u +97 18u = 97  7 18u = 90 u = 90/18 = 45/9 = 5 t = 7  u = 7  5 = 2 So the number has units place 5 and tens place 2 therefore the number is 25 Answer: 25 Directions: Solve the following word problems. 