SOLUTION: The ratio of the tens digit to the units digit of a two-digit number is 1:4. If the digits are reversed, the sum of the new number and the original number is 110. Find the origin

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: The ratio of the tens digit to the units digit of a two-digit number is 1:4. If the digits are reversed, the sum of the new number and the original number is 110. Find the origin      Log On

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Question 265665: The ratio of the tens digit to the units digit of a two-digit number is 1:4. If the digits are reversed, the sum of the new number and the original number is 110. Find the original number?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = tens digit
Let b = units digit
The number is 10a+%2B+b
With the digits reversed,
the number is 10b+%2B+a
given:
a%2Fb+=+1%2F4
10a+%2B+b+%2B+10b+%2B+a+=+110
-----------------------------
a+=+%281%2F4%29%2Ab
%2810%2F4%29%2Ab+%2B+b+%2B+10b+%2B+%281%2F4%29%2Ab+=+110
%2811%2F4%29%2Ab+%2B+11b+=+110
11b+%2B+44b+=+440
55b+=+440
b+=+8
and, since
a%2Fb+=+1%2F4
a%2F8+=+1%2F4
a+=+2
The original number is 28
check:
28+%2B+82+=+110
110+=+110
OK