A man wanted to get into his work building, but he had forgotten his code.

However, he did remember five clues. These are what those clues were:

The fifth number plus the third number equals fourteen.

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 ten.

The sum of all five numbers is 30.

What were the five numbers and in what order?

7,4,6,5,8

Suppose the code can be represented as:
ABCDE


where each letter represents some number from 0 through 9.


Write an equation for each statement:
E + C = 14
D = B + 1
A = 2*B - 1
B + C = 10
A+B+C+D+E = 30


Solve via your favorite method (algebra not shown):
A = 7, B = 4 C=6, D = 5, E = 8


Result:
74658

Write down what you know:

c + e = 14
d = b + 1
a = 2b - 1
b + c = 10
a + b + c + d + e = 30

Since b seems to be common, rewrite the last equation in terms of b:

(2b - 1) + b + (10 - b) + (b + 1) + (b + 4) = 30

Since c = 14 - e = 10 - b => e = b + 4

4b + 14 = 30 => 4b = 16 => b = 4

Finishing it off, we get:
a = 7; b = 4; c = 6; d = 5; e = 8

abcde is the number.

e+c = 14 [1]
d = b+1 [2]
a = 2b-1 [3]
b+c = 10 [4]
a+b+c+d+e = 30 [5]

Alright!
[x] > [y] means substitute [x] into [y]

[2] > [5] and [3] > [5]
(2b-1) + b + c + (b+1) + e = 30

4b+c+e = 30 [5*]

[1] > [5*]

4b + 14 = 30
b = 4 [6]

[6] > [2]
d=5
[6] > [3]
a=7
[6] > [4]
c=6 [7]

[7] > [1]
e=8