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Question 172206: “A man wanted to get into his work building, but he had forgotten his pin-code. However, he did remember five clues.
These are what those clues were:
The fifth number plus the third number equals 14.
The fourth number is one more than the second number.
The first number is one less than twice the second number.
The second number plus the third number equals 10.
The sum of all five numbers is 30.
What were the five numbers and in what order?”
Found 2 solutions by Mathtut, jvanfossen:
Answer by Mathtut(3670)   (Show Source):
You can put this solution on YOUR website! let a,b,c,d,e be 1st,2nd,3rd,4th,and 5th numbers respectively
:
e+c=14--->e+(b-10)=14--->e=-b+24..eq 1
d=b+1.............................eq 2
a=2b-1............................eq 3
b=c+10---->c=b-10.................eq 4
a+b+c+d+e=30
:
take the 1st four values e,d,a,and c from the 1st 4 equations and plug them into eq 5
:
(2b-1)+b+(b-10)+(b+1)+(-b+24)=30
:
4b+14=30
:
4b=16
:
 2nd number
:
 1st number
:
 3rd number
:
 4th number
:
 5th number
Answer by jvanfossen(1) (Show Source):
You can put this solution on YOUR website! e + c = 14 ; e + 10 - b = 14 ; e = b + 4 ; e = 4 + 4 = 8
d = b + 1 ; d = 4 + 1 = 5
a = 2b - 1 ; a = 2 (4) - 1 = 7
b + c = 10 ; c = 10 - b ; c = 10 - 4 = 6
and
a + b + c + d + e = 30
(2b - 1) + (b) + (10 - b) + (b + 1) + (b + 4) = 30 ; b = 4
check:
(2(4)-1) + (4) + (10 - 4) + (4 + 1) + (4 + 4) = 30
(7) + (4) + (6) + (5) + (8) = 30
30 = 30
a = 7; b = 4; c = 6; d = 5 and e = 8
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