SOLUTION: the sum of the digit of a three-place number is 16. if the digit are reversed and the resulting number added to the original number the sum is 1049. if the resulting number is subt

Question 640694: the sum of the digit of a three-place number is 16. if the digit are reversed and the resulting number added to the original number the sum is 1049. if the resulting number is subtracted from the original number the difference is 297. what is the number?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The three digits; x, y, z
then
100x+10y+z = "the original number"
:
Write an equation for each statement:
:
"the sum of the digit of a three-place number is 16."
x + y + z = 16
:
"if the digit are reversed and the resulting number added to the original
number the sum is 1049."
(100x + 10y + z) + (100z + 10y + x) = 1049
Combine like terms
100x + x + 10y + 10y + 100z + z = 1049
101x + 20y + 101z = 1049

"if the resulting number is subtracted from the original number the difference
is 297."
(100x + 10y + z) - (100z + 10y + x) = 297
100x + 10y + z - 100z - 10y - x = 297
100x - x + 10y - 10y + z - 100z = 297
99x - 99z = 297
Simplify divide by 99
x - z = 3
:
Multiply the 1st equation by 101 and subtract the 2nd equation
101x + 101y + 101z = 1616
101x + 20y + 101z = 1049
---------------------------Subtraction eliminates x and z, find y
0 + 81y + 0 = 567
y =
y = 7
:
Back to the 1st equation, replace y with 7
x + 7 + z = 16
x + z = 9; subtracted 7 from both sides
then
x + z = 9
x - z = 3
------------addition eliminates z, find x
2x = 12
x = 6
then we know x + z = 9
6 + z = 9
z = 3
:
original number: 673
:
:
Confirm this in the statement:
"the resulting number is subtracted from the original number the difference
is 297."\
673 - 376 = 297

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