Question 735609
The five digits: a, b, c, d, e
:
Write an equation for each statement:
:
" the first digit is one more than the second,
a = b+1
or
b = a-1
:
" the last is four fewer than the first,
e = a-4
:
" the second is more than the last,"
b > e
:
" the fourth is one more than the last?"
d = e+1
replace e with (a-4)
d = (a-4) + 1
d = a-3
:
" The sum of all the digits is 35."
a + b + c + d + e = 35
replace b with (a-1), replace e with (a-4); replace d with (a-3)
a + (a-1) + c + (a-3) + (a-4) = 35
combine like terms
4a + c - 8 = 35
4a + c = 35 + 8
4a + c = 43
c = -4a + 43
The only single digit integer solution is when a = 9, then c = 7
b = 9-1
b = 8
and
d = 9-3
d = 6
and
e = 9-4
e = 5
the  five digit number: 98765
;
:
See if that adds up
9 + 8 + 7 + 6 + 5 = 35