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Example: If twentyseven is added to a twodigit 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 twentyseven is added to a twodigit 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)  3equation 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 twentyseven is added to a twodigit 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. 