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Question 658460: The units digit of a number is 4 times the tens digit. If 54 is added to the number, the digits will be interchanged. Find the number.
Answer by kevwill(135)   (Show Source):
You can put this solution on YOUR website! 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
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