Answer:
45
Step-by-step explanation:
A number consists of 2 digits whose sum is 9 => x + y = 9
If the order of the numbers is inverted, the result is equal to the given number plus 9 units => (10*y + x) + 9 = (10*x + y)
Thus:
x + y = 9 => multiply by -9 => 9*y + 9*x = 81
10*y + x + 9 = 10*x + y => 9*y - 9*x = -9
We are left then that:
9*y + 9*x = 81 (1)
9*y - 9*x = -9 (2)
we add both equations
18y = 72
y = 72/18 = 4
replacing
x + y = 9
x + 4 = 9
x = 5
Therefore the number is (10y + x) => (10 * 4 + 5) => 45
