Question 956856: 1) The sum of a 3-digit number is 18. If he second and third digits are interchanged, the number would be increased by 36. If the first and third digits are interchanged, the new number would be 99 less than the original number. Find the number. 2) The sum of a 3-digit number is 14. If the digits are reversed and the resulting number is added to the original number, the sum is 1171. If the resulting number is subtracted from the original number, the difference is ten times the hundreds digit more than 201 times the tens digit. Find the original number.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! let a = the 100's digit
let b = the 10's digit
let c = the units
then
100a+10b+c = the original number
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Write an equation for each statement, simplify as much as possible
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1) The sum of a 3-digit number is 18.
a b + c = 18
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If the second and third digits are interchanged, the number would be increased by 36.
100a + 10c + b = 100a +10b + c + 36
Subtract 100a from both sides
10c + b = 10b + c + 36
Combine like terms
10c - c = 10b - b + 36
9c = 9b + 36
simplify, divide equation by 9
c = b + 4
or
b = c - 4
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If the first and third digits are interchanged, the new number would be 99 less than the original number.
100c + 10b + a = 100a + 10b + c - 99
subtract 10b from both sides
100c + a = 100a + c - 99
100c - c = 100a - a - 99
99c = 99a - 99
divide by 99
c = a - 1
or
a = c + 1
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Find the number.
substitute (c-4) for b, and (c+1) for a in the 1st equation
(c+1) + (c-4) + c = 18
3c - 3 = 18
3c = 18 +3
3c = 21
c = 7
find a & b
a = 7 + 1
a = 8
and
b = 7 - 4
b = 3
therefore our original number is 837
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Confirm this in the 2nd statement
"If the second and third digits are interchanged, the number would be increased by 36."
873 = 837 + 36
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I have tried to make this an understandable method so that you can do the 2nd one by yourself. Let me know how you do. ankor@att.net
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2) The sum of a 3-digit number is 14. If the digits are reversed and the resulting number is added to the original number, the sum is 1171. If the resulting number is subtracted from the original number, the difference is ten times the hundreds digit more than 201 times the tens digit. Find the original number.
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