SOLUTION: H E L P !!!!!! How do you solve: A three-digit number is 198 more than the number formed by reversing the digits. The 100's digit is 3 more than the 10's digit. The sum of the

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: H E L P !!!!!! How do you solve: A three-digit number is 198 more than the number formed by reversing the digits. The 100's digit is 3 more than the 10's digit. The sum of the      Log On


   

Question 71783: H E L P !!!!!! How do you solve:
A three-digit number is 198 more than the number formed by reversing the digits. The 100's digit is 3 more than the 10's digit. The sum of the digits is 16. What is the original number?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A three-digit number is 198 more than the number formed by reversing the digits.
The 100's digit is 3 more than the 10's digit. The sum of the digits is 16. What
is the original number?
:
Let x = 100's digit of original number
Let y = 10's digit
Let z = 1's digit of original number:
:
Original number - Reversed number = 198
(100x + 10y + z) - (100z + 10y + x) = 198
:
100x + 10y + z - 100z - 10y - x = 198
:
99x - 99z = 198
:
Simplify, divide by 99
x - z = 2
:
"The 100's digit is 3 more than the 10's digit."
x = y + 3
x - y = 3
:
"The sum of the digits is 16"
x + y + z = 16
:
Three equations:
x + 0y - 1z = 2
x - 1y + 0z = 3
x + 1y + 1z = 16
------------------ adding eliminates y and z
3x +0y + 0z = 21
3x = 21
x = 21/3
x = 7
:
Find z using; x - z = 2
7 - z = 2
z = 5
:
Find y using: x - y = 3
7 - y = 3
y = 4
:
our number is 745
:
Check: 745 - 547 = 198