# Two-digit number

The digit sum of thinking two-digit natural numbers is 11. When it exchanges a sequence of digits, given a number that is 27 less than the thinking number, find out which number I think.

x =  74

## Step-by-step explanation:

x = 10·a+b
a+b = 11
10·b+a = x - 27

10a+b-x = 0
a+b = 11
a+10b-x = -27

Row 2 - 1/10 · Row 1 → Row 2
10a+b-x = 0
0.9b+0.1x = 11
a+10b-x = -27

Row 3 - 1/10 · Row 1 → Row 3
10a+b-x = 0
0.9b+0.1x = 11
9.9b-0.9x = -27

Pivot: Row 2 ↔ Row 3
10a+b-x = 0
9.9b-0.9x = -27
0.9b+0.1x = 11

Row 3 - 0.9/9.9 · Row 2 → Row 3
10a+b-x = 0
9.9b-0.9x = -27
0.182x = 13.455

x = 13.45454545/0.18181818 = 74
b = -27+0.9x/9.9 = -27+0.9 · 74/9.9 = 4
a = 0-b+x/10 = 0-4+74/10 = 7

a = 7
b = 4
x = 74

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