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Question 410128: the sum of a four digits of an even number is 10 the digit in the hundreds place is 2 more than the digit in the tens place but 1 less than the digit in the ones place what number am i
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! the sum of a four digits of an even number is 10
a + b + c + d = 10
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"the digit in the hundreds place is 2 more than the digit in the tens place"
b = c + 2
c = (b-2)
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"but 1 less than the digit in the ones place what number"
b = d - 1
d = (b+1)
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a + b + c + d = 10
Replace c and d
a + b + (b-2) + (b+1) = 10
a + 3b - 1 = 10
a + 3b = 10 + 1
a + 3b = 11
a = -3b + 11
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From this, we only have three positive integer possibilities
b = 1, a = 8, not possible, (because of the number digits)
b = 2, a = 5, also not possible, (then c = 0)
b = 3, a = 2, this must be the answer
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Our 4 digit number: 2314 (which adds up to 10)
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