Word Problems of Linear Equations
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 Word Problems of Linear Equations Example: The sum of a two digit number and the number obtained by reversing the order of its digits is 121, and the two digits differ by 3. Find the number.
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 Solution: Let the digit in the unit's place be x and the digit at the ten's place be y. Then,      Number = 10y + x The number obtained by reversing the order of the digits is 10x + y. According to the given conditions, you have (10y + x) + (10x + y) = 121  11 (x +  y) = 121  x + y = 11 And, x - y = 3 [Difference of digits is 3] Thus, you have the following sets of simultaneous equations:            x + y = 11......(i)     and, x - y = 3 .......(ii)     or,            x + y = 11......(iii)     and, x - y = -3 ......(iv) on solving equations (i) and (ii) you get x = 7,  y = 4 on solving equations (iii) and (iv) you get x = 4,  y = 7 When x = 7, y = 4, you have     Number = 10y + x = 10 * 4 + 7 = 47. When x = 4, y = 7, you have     Number = 10y + x = 10 * 7 + 4 = 74. Hence, the required number is either 47 or 74.

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