Question 143781

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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