SOLUTION: The sum of the digits of a three digit number is 17. The tens digit is 12 less than the sum of the units digit and twice the hundred digits. If the units digit and the hundreds dig

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Question 1100738: The sum of the digits of a three digit number is 17. The tens digit is 12 less than the sum of the units digit and twice the hundred digits. If the units digit and the hundreds digit are reversed, the new number is 297 less than the original number. What's the original number?

Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
If you use h for hundreds digit, t for tens digit and u for units digit, then the description literally gives this system of equations:
system%28h%2Bt%2Bu=17%2Ct=u%2B2h-12%2Ch%2B10t%2B100u=100h%2B10t%2Bu-297%29

You should be able to simplify and solve the system and get whole number results for h, t, and u.

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Simplified System: system%28h%2Bt%2Bu=17%2Ct=u%2B2h-12%2Ch-u=3%29

Substitute for t:
system%283h%2B2u=29%2Ch-u=3%29

Using Elimination Method,
system%28h=7%2Cu=4%2Cand_then%2Ct=6%29

The three-digit number: 764