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Question 946713: What is a six digit number in which the first digit is 1 more than the third and the second digit is one less than the fourth the 5th digit is one less than the third and the 6 digit is one more than the fourth the sum of the second and third digit equal the first the sum of all digits is 30
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Probably a lot of ways to do this, Write an equation for each statement
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What is a 6 digit number
let the six digits be: a, b, c, d, e, f
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in which the 1st digit is 1 more than the 3rd,
a = c + 1
or
c = a - 1
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the 2nd digit is 1 less than the 4th,
b = d - 1
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the 5th digit is 1 less than the 3rd,
e = c - 1
replace c with (a-1)
e = a - 1 - 1
e = a - 2
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and the 6th digit is 1 more than the 4th.
f = d + 1
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The sum of the 2nd and 3rd digit equals the 1st.
b + c = a
replace b with (d-1)
d - 1 + c = a
replace c with (a-1)
d - 1 + a - 1 = a
d - 2 = a - a
d = 2
then we know f = d + 1, therefore
f = 2 + 1
f = 3
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The sum of all digits is 30.
a + b + c + d + e + f = 30
replace b+c with a and d with 2, replace f with 3
a + a + 2 + e + 3 = 30
2a + e = 30 - 2 = 3
2a + e = 25
replace e with (a-2)
2a + a - 2 = 25
3a = 25 + 2
3a = 27
a = 27/3
a = 9
Now we know: 9 b c 2 e 3
find e using e = a - 2
e = 9 - 2
e = 7
find c using c = a - 1
c = 9 - 1
c = 8
Find b using the total being 30
9 + b + 8 + 2 + 7 + 3 = 30
b + 29 = 30
b = 1
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Our number then: 9 1 8 2 7 3
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