Question 1172026: The sum of the digits of a three-digits number is 17. The sum of the first and third is one more than three times the second digit. If the digits are reversed, the new number is 297 greater than the original number. Find the original number. (Hint: Let x be the first digit, y the second digit and be the third digit of the original number.)
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! The sum of the digits of a three-digits number is 17.
The sum of the first and third is one more than three times the second digit.
If the digits are reversed, the new number is 297 greater than the original number.
Find the original number. (Hint: Let x be the first digit, y the second digit and z be the third digit of the original number.)
:
write an equation for each statement, we can reearrange the equations for elimination.
:
The sum of the digits of a three-digits number is 17.
x + y + z = 17
The sum of the first and third is one more than three times the second digit.
x + z = 3y + 1
x - 3y + z = 1
If the digits are reversed, the new number is 297 greater than the original number.
100x + 10y + z = 100z + 10y + x - 297
100x - x + 10y - 10y + z - 100z = - 297
99x - 99z = - 297
simplify, divide by 99
x - z = -3
:
use elimination on the first two equations to find y
x + y + z = 17
x - 3y + z = 1
-----------------subtraction eliminates x & y, find y
0 + 4y + 0 = 16
y = 16/4
y = 4
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Replace y with 4 in the first equation
x + 4 + z = 17
x + z = 17 - 4
x + z = 13
Use elimination with the 3rd equation
x + z = 13
x - z = -3
-------------addition eliminates z, find x
2x + 0 = 10
x = 10/2
x = 5
Find z
5 + z = 13
z = 13 - 5
z = 8
:
The original number 548
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Check this in the last statement
"If the digits are reversed, the new number is 297 greater than the original number."
548 = 845 - 297
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