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Question 495910: A five digit no whose third digit is one greater than the sum of the first two digits, and the third digit is double the fourth digit ,and fourth digit is double the fifth digit, and second digit is greater than first digit by 5. and if we multiply fourth and fifth digit we get third digit.
need solution in detail
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! 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
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