A number consists of two digits. The sum of digits is 9. If 63 is subtracted from the number, its digits are interchanged. Find the number.
Question
A number consists of two digits.
The sum of digits is 9.
If 63 is subtracted from the number, its digits are interchanged.
Find the number.
Solution
Let's denote the tens digit as "x" and the units digit as "y".
From the problem, we know two things:
-
x + y = 9 (The sum of the digits is 9)
-
10x + y - 63 = 10y + x (If 63 is subtracted from the number, its digits are interchanged)
Now, we can solve these equations step by step:
First, simplify the second equation:
9x - 9y = 63
Divide through by 9:
x - y = 7
Now we have a system of two equations:
x + y = 9
x - y = 7
Add these two equations together:
2x = 16
Divide by 2:
x = 8
Substitute x = 8 into the first equation:
8 + y = 9
Solve for y:
y = 1
So, the number is 81.
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