Question 735609: What is the five digit number in which the first digit is one more than the second, the last is four fewer than the first, the second is more than the last, and the fourth is one more than the last? The sum of all the digits is 35.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! 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
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