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when its digits are reversed, a particular positive two-digit integer is increased by 20%. what is the original number?
Let 10x + y = the original two digit number
10y + x = that number with digits reversed
1.2 * a number = a number increased by 20%
1.2(10x + y) = 10y + x
12x + 1.2y = 10y + x
12x - x = 10y - 1.2y
11x = 8.8y
Divide both sides by 11
x = .8y
The only single digit integer that would satisfy this equation:
y = 5, then x = 4
45 = the number
54 = 1.2(45); the number reversed