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### Math Word Problems - GED, PSAT, SAT, ACT, GRE Preparation3.16 Word Problems - Digits

 Method 2: Step 1: Write all the equations in terms of one variable. Step 2: Solve the equation Example : The tens digit of a two-digit number is two more than the ones digit. The number is thirty more than four times the sum of the digits. What is the number? Solution: Let the ones digit be 'x' Tens digit is two more than the ones digit = x + 2 The number is 10(x+2) + x Thirty more than four times the sum of the digits so 4(x + x + 2) +30 Therefore, the number is thirty more than four times the sum of the digits can be written as 10(x + 2) + x = 4(x + x + 2) + 30 10(x + 2) + x = 4(2x + 2) + 30 10x + 20 + x = 8x + 8 + 30 11x + 20 = 8x + 38 11x - 8x = 38 - 20 3x = 18 x = 18/3 = 6 the number in tens place is x + 2 = 6 + 2 = 8 The number is 86. Directions: Solve the following word problems.
 Q 1: The ten's digit of a two digit number exceeds the unit's digit by 4. The sum of the digits is 10. Find the number. (Hint: Let the units digit = x Ten's digit = x + 4 x + x + 4 = 10 ) 735140 Q 2: The sum of the digits of a two digit number is 8. If 18 is added to the number, the digits are reversed. Find the number. (Hint: Let the digit is units place = xDigit in the ten's palce = 8 - x The number = 10(8 - x) + x when the digits are reversed the number = 10x + (8 - x) Solve the equation: 10(8 - x) + x + 18 = 10x + (8 - x) )263517 Q 3: The sum of two digits of a two digit number is 15. If 9 is added to it, the digits are reversed. Find the number. (Hint: Let the digit in the unit's place = x then the Tens place = 15 - x. The number 10(15 - x) + x = 150 - 10x + x= 150 - 9xIf the digits are reversed, the number = 10x + 15 - x = 9x + 15 Solving 150 - 9x + 9 = 9x + 15 ) 966978 Q 4: The difference between ten's digit and unit's digit of a two digit number is 6. When the digits are reversed the new number added to the original number becomes 88. Find the original number. (Hint: Let the units digit be x, then the ten's digit = x + 6 The number is 10(x + 6) + x when the digits are reversed, the number is 10x + (x + 6)Solving the equation: 10(x + 6) + x + 10x + (x + 6)= 88) 829371 Question 5: This question is available to subscribers only! Question 6: This question is available to subscribers only!