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| 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. |