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Question 324543: ''the sum of 3 digits is 5. the first and last digits are the same. if the middle digit is exchanged with the first digit, the new number is 90 less than the original number. find the original number.''
Found 2 solutions by stanbon, ankor@dixie-net.com:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! ''the sum of 3 digits is 5. the first and last digits are the same. if the middle digit is exchanged with the first digit, the new number is 90 less than the original number. find the original number.''
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Let the number be x*10^2 + y*10 + z
After exhanging 1st and 2nd the number is y*10^2 + x*10 + z
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Equations:
x + y + z = 5
x = z
100x + 10y + z -(100y + 10x + z) = 90
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Modify:
2x + y = 5
90x -90y = 90
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Modify:
2x + y = 5
x - y = 1
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Add and solve for "x":
3x = 6
x = 2
Then z = 2
Then y = 1
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Number is 212
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Cheers,
Stan H.
Answer by ankor@dixie-net.com(22740)  (Show Source):
You can put this solution on YOUR website! ''the sum of 3 digits is 5. the first and last digits are the same.
if the middle digit is exchanged with the first digit, the new number
is 90 less than the original number.
find the original number.''
:
The three digits: x, y, z
then
100x + 10y + z = original number
:
Write an equation for each statement:
:
"''the sum of 3 digits is 5."
x + y + z = 5
:
"the first and last digits are the same."
x = z
therefore
x + y + z = 5
2x + y = 5
;
"if the middle digit is exchanged with the first digit, the new number is 90
less than the original number."
100y + 10x + z = 100x + 10y + z - 90
100y - 10y + z - z = 100x - 10x - 90
90y = 90x - 90
Simplify divide by 90
y = x - 1
or
x - y = 1
:
Use the two simplified equations for elimination:
2x + y = 5
x - y = 1
-----------Adding eliminates y, find x
3x = 6
x = 2
then
z = 2
then, since the three digits add up to 5:
y = 1
:
find the original number.'': 212 is the original number
:
:
Check solution in the statement:
" if the middle digit is exchanged with the first digit, the new number is 90 less than the original number."
122 = 212 - 90
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