Question 495910
The five digits: a, b, c, d, e
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Write an equation for each statement
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"A five digit no whose third digit is one greater than the sum of the first two digits,"
c = a + b + 1
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"and the third digit is double the fourth digit"
c = 2d
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"and fourth digit is double the fifth digit,"
d = 2e
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"and second digit is greater than first digit by 5."
b = a + 5
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"if we multiply fourth and fifth digit we get third digit."
d*e = c
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Let's see if we can sort something out with this equation
replace c with 2d (from the 2nd equation)
d*e = 2d
divide both sides by d and we have
e = 2
then from the 3rd equation
d = 2e
d = 2(2)
d = 4
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using the last equation
d*e = c
4*2 = c
c = 8
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we have _ _ 8 4 2 so far, find a and b
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with the 1st equation arrange it as follows, replace c with 8
a + b + 1 = c
a + b + 1 = 8
a + b = 8 - 1
a + b = 7
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Arrange the 4th equation
b = a + 5
-a + b = 5
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Use elimination on these two derived equations
a + b = 7
-a+ b = 5
------------addition eliminates a, find b
2b = 12
b = 6
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Find a using a + b = 7
a + 6 = 7
a = 7 - 6
a = 1
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Our number: 1 6 8 4 2
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You can check that these values satisfy each of our 4 equations