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Question 633693: In a certain three digit number, the hundreds digit is the sum of the other two digits. If the units and tens digits of this number are interchanged,the new number is 9 more than the original number. If the hundreds and ten digits of the original number are interchanged, the new number is 360 less than the original number. Find the original number.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! The three digits: a, b, c; write an equation for each statement
Simplify each equation as much as possible
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In a certain three digit number,
100a + 10b + c
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the hundreds digit is the sum of the other two digits.
a = b + c
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If the units and tens digits of this number are interchanged,the new number
is 9 more than the original number.
100a + 10c + b = 100a + 10b + c + 9
Subtract 100a from both sides
10c + b = 10b + c + 9
10c - c = 10b - b + 9
9c = 9b + 9
simplify, divide by 9
c = b + 1
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If the hundreds and ten digits of the original number are interchanged,
the new number is 360 less than the original number.
100b + 10a + c = 100a + 10b + c - 360
subtract c from both sides
100b + 10a = 100a + 10b - 360
100b - 10b = 100a - 10a - 360
90b = 90a - 360
Simplify, divide by 90
b = a - 4
or
a = b + 4
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Using the equation: a = b + c, replace a and c
(b+4) = b + (b+1)
4 - 1 = 2b - b
3 = b
then
a = 3 + 4
a = 7
and
c = 3 + 1
c = 4
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734 is the original number
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You can confirm this solution in the last two statements
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