word problem
posted by emma .
in a two digit number, the sum of the digit is 8. the different between this number and the number with the digit reversed is 54, what is the number.

n m = 10 n + m
n+m = 8
m n = n + 10 m
n + 10 m  (10 n + m) = 54
9 n + 9 m = 54
n + m = 6
but
+n + m = 8
 add
0 +2m = 14
m = 7
n = 1
so
17 
original:
unit digit  x
tens digit  8x
the number: 10(8x) + x
the number reversed: 10x + (8x)
10x + 8x  (10(8x) + x) = 54
10x + 8 x  80 + 10x  x = 54
18x = 126
x = 7
unit digit = 7
tens digit = 1
original number 17
number reversed 71
or
original number is 71
number reversed is 17
in both cases the difference between them is 54