The number with the given characteristics 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
y = x + 6
The relationship between the number and the reverse is
2(10x + y + 10y + x) = 6 + 10 * (10x + y)
Simplify the second equation
2(11x + 11y) = 6 + 100x + 10y
Open the brackets
22x + 22y = 6 + 100x + 10y
Substitute y = x + 6
22x + 22(x + 6) = 6 + 100x + 10(x + 6)
Expand
22x + 22x + 132 = 6 + 100x + 10x + 60
Collect like terms
22x + 22x - 100x - 10x = 6 + 60 - 132
Evaluate the like terms
-66x = -66
Divide by -66
x = 1
Substitute x = 1 in y = x + 6
y = 1 + 6
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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