Question

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.

Answer 1

45

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