simultaneous equation

A certain number of two digits is three times the sum of its digits and if 45 be added to it the digits will be reversed, find the number.


Answer:
Let x be the digit in the tens place, y the digits in the units place.

Hence the equations are:

10x + y = 3(x + y) --------(1)
10x + y + 45 = 10y + x--------(2)

Solving (1), we have 7x - 2y = 0  ---(3)

Solving (2), we have y - x = 5

or, 2y - 2x = 10  -------(4)

Solving (3) and (4), we get , x = 2.
Therefore, y = 7.

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