Question 327350
Thanks for re-asking this question ^.^

Let the three digit number be represented by the variables xyz, with x being the values in the hundreds place, y being the number in the tens place, and z being the number in the ones place. Rewriting the problem into equation form you get the following. "The sum of a three-digit number is 15": {{{x+y+z=15}}}. "If the digits are reversed and the resulting number is added to the original the sum is 1029": {{{(xyz)+(zyx)=1029}}}. "The resulting number is subtracted from the original the difference is 693": {{{(xyz)-(zyx)=693}}}. (Note: it's great we have three equations because we have three unknown variables. If we have more unknown variables than equations, we won't be able to solve for the variables =)) Okay, let's solve for the variables. You can add the last two equations together to get: {{{(xyz)+(zyx) + xyz)-(zyx)=1029+693}}}. You get {{{2xyz=1722}}}. Divide both sides by 2 to get {{{xyz=861}}}. Now you plug this back in and solve for zyx to get zyx=168 =]
Both of these numbers are reverse of one another and if you add up their three digits you get 15 as a sum! Thus, the three digit number is 861. 
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