SOLUTION: a certain number, if two digits equals 4 times thew sum of its digits. the number made by reversing the order of the digits is 27 greater than the given number. what is the number?

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Question 161736: a certain number, if two digits equals 4 times thew sum of its digits. the number made by reversing the order of the digits is 27 greater than the given number. what is the number?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let's call the number in the tens place A and the number in the ones place B.
The number would be AB or 10*A+B.
1.10A%2BB=4%2A%28A%2BB%29
If the number is reversed then,
2.10B%2BA=27%2B%2810A%2BB%29
Let's simplify both equations,
1.10A%2BB=4A%2B4B
1.6A-3B=0
and now eq. 2,
2.10B%2BA=27%2B%2810A%2BB%29
2.-9A%2B9B=27
Let's multiply eq. 1 by 3 and add to eq. 2,
then we can solve for A.
18A-9B%2B%28-9A%29%2B9B=0%2B27
9A=27
A=3
Now use eq. 1 to solve for B.
1.6A-3B=0
18-3B=0
-3B=-18
B=6
The original number is 36, the reversed order number is 63.
Check the answer.
36+27=63
63=63.
True statement.
Good answer.