Un número consta de dos cifras cuya suma es 9. Si se invierten el orden de las cifras el resultado es igual al número dado más 9 unidades. Encuentra dicho número.

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