The number with the given properties is 17
How to determine the numbers?
Let the tens be x and the units be y.
So, the number is 10x + y
The relationship between the digits is
[tex]y = x + 6[/tex]
The relationship between the number and the reverse is
[tex]2(10x + y + 10y + x) = 6 + 10 * (10x + y)[/tex]
Simplify the second equation
[tex]2(11x + 11y) = 6 + 100x + 10y[/tex]
Open the brackets
[tex]22x + 22y = 6 + 100x + 10y[/tex]
Substitute y = x + 6
[tex]22x + 22(x + 6) = 6 + 100x + 10(x + 6)[/tex]
Expand
[tex]22x + 22x + 132 = 6 + 100x + 10x + 60[/tex]
Collect like terms
[tex]22x + 22x - 100x - 10x = 6 + 60 - 132[/tex]
Evaluate the like terms
[tex]-66x = -66[/tex]
Divide by -66
x = 1
Substitute x = 1 in y = x + 6
[tex]y = 1 + 6[/tex]
y = 7
Recall that the number is 10x + y
So, we have
Number = 10 * 1 + 7
Evaluate
Number = 17
Hence, the number is 17
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