Posted by **emma** on Monday, November 21, 2011 at 7:06pm.

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**, Monday, November 21, 2011 at 7:11pm
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**, Monday, November 21, 2011 at 7:12pm
original:

unit digit -- x

tens digit -- 8-x

the number: 10(8-x) + x

the number reversed: 10x + (8-x)

10x + 8-x - (10(8-x) + 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

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