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sattari [20]
3 years ago
7

The sum of the digits of a two-digit number is 12. The number formed by interchanging the digits is 54 more than the original nu

mber. What is the original number?
Mathematics
1 answer:
-BARSIC- [3]3 years ago
8 0
Let X and Y be the digits.
If a two-digit number is written XY, then its value is 10x+y.
When the digits of the number are interchanged, it's YX, and its value is 10y+x.

The sum of the digits is 12.
The number formed by interchaning the digits is 54 more than the original number.

x+y=12 \\
10x+y+54=10y+x \\ \\
x+y=12 \\
10x-x+y-10y=-54 \\ \\
x+y=12 \\
9x-9y=-54 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\div 9 \\ \\
x+y=12 \\
\underline{x-y=-6} \\
x+x=12-6 \\
2x=6 \\
x=\frac{6}{2} \\
x=3 \\ \\
x+y=12 \\
3+y=12 \\
y=12-3 \\
y=9

The digits X and Y are 3 and 9, so the original number is 39.
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I think your question is missed of key information, allow me to add in and hope it will fit the original one.  Please have a look at the attached photo

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