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Question 396868: A number has four digits.The sum of the first and last digits is twice the second digit.The second digit is 2 less than the third digit.The last digit
is twice the first digit.Some of the digits are alike.What is the number?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Four digits: w,x,y,z
:
Write an equation for each statement
:
"The sum of the first and last digits is twice the second digit."
w + z = 2x
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"The second digit is 2 less than the third digit."
x = y - 2
y = x + 2
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"The last digit is twice the first digit."
z = 2w
From this we know w < 5
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In the 1st equation, replace z with 2w
w + 2w = 2x
3w = 2x
w =  x
We know w<5 therefore x=3, w=2, or x=6, w=4
If w=2, x=3, z=4: 2 3 _ 4
It w=4, x=6, z=8: 4 6 _ 8
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Assume that y is the same as one of the other numbers:
If x=3: y = 3 + 2 = 5, not the same as any other numbers
If x=6: y = 6 + 2 = 8, same when z=8
:
The number should be 4 6 8 8
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