A two-digit number is such that twice the tens digit is 6 greater than the units digit. When the digits are reversed, the number is increased by 9. Find the number.

10x+y - a two digit number x - ten digit y - unit digit
[2x=y+6\ 10y+x=10x+y+9\\ y-2x=-6\ 9y-9x=9\\ y-2x=-6\ y-x=1\\ y-2x=-6\ -y+x=-1\ ------\ -x=-7\ x=7\\ y-7=1\ y=8\\ 10\cdot7+8=\boxed{78}
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Answered by konrad509 | 2024-06-10

The two-digit number is 78. This was found by determining the digits based on two mathematical conditions given in the problem. When the digits are reversed, the number increases by 9, confirming that the answer is correct.
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Answered by konrad509 | 2024-12-26