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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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