Question 658460
Let x by the tens digit and y be the units digit.  Then from the first sentence:
y = 4x
And from the second sentence:
10x + y + 54 = 10y + x
Substituting y = 4x into the second equation gives:
10x + 4x + 54 = 10*(4x) + x
Combining like terms:
14x + 54 = 41x
Subtracting 14x from both sides and reversing the equation:
27x = 54
Dividing both sides by 27:
x = 2
So x = 2, y = 4*2 = 8, and the number is 28.  28 + 54 = 82