Posted by emma on .
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.

word problem 
Damon,
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 
word problem 
Reiny,
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