Question 143781: 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?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website!
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Let code (in order) = a,b,c,d,e
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Try to get everything in terms of c, seems like a good approach
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Write an equation for all five statements:
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1."The fifth number plus the third number equals fourteen."
e + c = 14
or
e = (14-c)
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2."The fourth number is one more than the second number."
d = b + 1
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3."The first number is one less than twice the second number."
a = 2b - 1
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4."The second number plus the third number equals ten."
b + c = 10
or
b = (10-c)
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5."The sum of all five numbers is 30."
a + b + c + d + e = 30
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Using Statements 2 and 4 we can substitute (10-c) for b
d = b + 1
d = (10-c) + 1
d = (11-c)
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Using equations from statements 3 & 4, we can substitute (10-c) for b again:
a = 2b -1
a = 2(10-c) - 1
a = 20 - 2c - 1
a = (19-2c)
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We got a, b, d, and e in terms of c, substitute in equation 5
a + b + c + d + e = 30
(19-2c) + (10-c) + c + (11-c + (14-c) = 30
simplify
-2c - c + c - c - c + 19 + 10 + 14 + 11 = 30
-4c + 54 = 30
-4c = 30 - 54
-4c = -24
4c = 24; multiplied equation by -1
c = 24/4
c = +6
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What were the five numbers and in what order
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Using the equations find the other numbers:
a = 19 - 2(6)
a = 7
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b = 10 - 6
b = 4
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c = 6
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d = 11-6
d = 5
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e = 14 - 6
e = 8
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See if they satisfy statement 5
7 + 4 + 6 + 5 + 8 = 30
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His code number should be 74658
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