SOLUTION: The product of a two-digit nimber and its tens digit is 54. Fing the number if the sum of the digits when added to the number gives a result of 36.

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Question 165706: The product of a two-digit nimber and its tens digit is 54. Fing the number if the sum of the digits when added to the number gives a result of 36.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Call the units digit n
Call the tens digit m
The number is 10m+%2Bn
given:
(1) %2810m+%2B+n%29%2Am+=+54
(2) m+%2B+n+%2B+10m+%2B+n+=+36
from (2):
11m+%2B+2n+=+36
2n+=+36+-+11m
n+=+18+-+%2811%2F2%29%2Am
Substitute this in (1)
%2810m+%2B+18+-+%2811%2F2%29%2Am%29%2Am+=+54
10m%5E2+%2B+18m+-+%2811%2F2%29m%5E2+=+54
%289%2F2%29m%5E2+%2B+18m+-+54+=+0
Multiply both sides by 2
9m%5E2+%2B+36m+-+108+=+0
Divide both sides by 9
m%5E2+%2B+4m+-+12+=+0
%28m+-+2%29%28m+%2B+6%29+=+0 (just by looking at it)
m+=+2 makes sense because it is (+)
(2) m+%2B+n+%2B+10m+%2B+n+=+36
(2) 2+%2B+n+%2B+10%2A2+%2B+n+=+36
2n+%2B+22+=+36
2n+=+14
n+=+7
The number is 27