The digit in tens place of a two number is three times that in the ones place. If the digits are reversed the new number will be 36 less than the original number. Find the number?

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Mark Mottian answered
Let y represent the units digit. Let x represent the tens digit.  Formulate Equations:  1. x = 3y   (the tens digit is 3 times the unit digit) 2. 10y + x = 10x + y + 36  (if the digits are reversed, the new number will be 36 less thant the orginal number)  Simplify Equations:  Equation 1: X = 3y  x - 3y = 3y - 3y  (subtract 3y) x - 3y = 0  Equation 2: 10y + x = 10x + y + 36  10y - y + x - 10x = 10x - 10x + y - y + 36  (subtract y; subtract 10x) 9y - 9x = 36  (collect terms)  9y/9 - 9x/9 = 36/9  (divide each term by 9) y - x = 4  (simplify)  Gaussian Elmination  (x - 3y) + (y - x) = (4 + 0)  (add equation 1 and 2 together) -2y = 4  (collect terms) -2y/-2 = 4/-2  (divide by -2) y = -2  (simplify)  x = -2 * 3 x = -6  The number you seek will be: (-6 * 10) + (-2) = -62

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