Question

In a two digit number, the tens digit is 2 less than the units digit multiplied by 3. The reversed number is half of the original number plus 1/2. What is the original number?

Answer 1

73

Explanation:

Original number: XY

x = 3y - 2

10y + x = (10x + y) / 2 + 1/2

substitution: 10y + 3y - 2 = 13y - 2 = (10 * (3y - 2) + y) / 2 + 1/2

* 2 both sides and simplify: 26y - 4 = 31y - 19

31y - 26y = -4 + 19

5y = 15

y = 3

x = 7

Original number: 73