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### Math Word Problems - GED, PSAT, SAT, ACT, GRE Preparation3.17 Word Problems - Digit - 2

 Example: If twenty-seven is added to a two-digit number, the original number will be reversed. The number is three less than four times the sum of its digits. What is the number? Solution: Let 'u' be the number in the units place and 't' be the number in the tens place. The number can be written as 10t + u If twenty-seven is added to a two-digit number, the original number will be reversed: 10t + u + 27 = 10u + t The number is three less than four times the sum of its digits: 10t + u = 4(t + u) - 3 10t + u + 27 = 10u + t -----------equation 1 10t + u = 4(t + u) - 3-------------equation 2 10t + u + 27 = 10u + t ----------- equation 1 10t - t = 10u - u - 27 9t = 9u - 27 t = u - 3 10t + u = 4(t + u) - 3 ----------- equation 2 10t + u = 4t + 4u - 3 6t = 3u - 3 substituting t = u - 3 in the above equation we have 2(u - 3) = u - 1 2u - 6 = u - 1 u = 6 - 1 = 5 t = u - 3 = 5 - 3 = 2 The two digit number is 25 Verification: If twenty-seven is added to a two-digit number, the original number will be reversed: 25 + 27 = 52 52 is a reverse of 25 The number is three less than four times the sum of its digits 4(2+5)-3 = 4(7) - 3 = 28 - 3 = 25 Directions: Solve the following word problems.
 Q 1: The tens digit is 2 less than the units digit. If the digit are reversed, the sum of the reversed number and the original number is 154. Find the original number.847668 Q 2: A three digit number has a tens digit 2 greater than the units digit and a hundreds digit 1 greater than the tens digit. The sum of the tens and hundreds digits is three times the units digit. What is the number?786875578 Q 3: The ratio of the units digit to the tens digit of a two digit number is one half. The tens digit is 2 more than the units digit. Find the number.654236 Q 4: If you switch the ones digit by the tens digit, the sum of the 2 numbers will be 55. The ones digit is 3 more that the tens digit. What is the number. (Hint: Let u be the number in the units place and t be the number in the tens place. The number can be written as 10t + u. If the number is reversed then it will be 10 u + t. The sum of the number and its switch equals 55 implies 10t + u + 10u + t = 55. The other equation can be written as u = 3 + t. Solve both equations to find u and t and the number.)144125 Question 5: This question is available to subscribers only! Question 6: This question is available to subscribers only!