SOLUTION: “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 fif

Algebra ->  Algebra  -> Distributive-associative-commutative-properties -> SOLUTION: “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 fif      Log On

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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) About Me  (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
:
highlight%28b=4%292nd number
:
highlight%28a=2%284%29-1=7%291st number
:
highlight%28c=4-10=-6%293rd number
:
highlight%28d=4%2B1=5%294th number
:
highlight%28e=-4%2B24=20%295th number

Answer by jvanfossen(1) About Me  (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