Question 172652
You're on the right track. You have 2 of the three equations needed to solve this problem. Why are 3 equations needed? You have 3 variables, so you need 3 equations. 



Since "The tens digit exceeds the hundreds digit by the same amount that the units digit exceeds the tens digit", this means that the third equation is {{{t-h=u-t}}}



{{{t-h=u-t}}} Start with the third equation



{{{t=u-t+h}}} Add {{{h}}} to both sides.



{{{t+t=u+h}}} Add {{{t}}} to both sides.



{{{t+t-u=h}}} Subtract {{{u}}} from both sides.



{{{2t-u=h}}} Combine like terms.



{{{h=2t-u}}} Rearrange the equation.



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{{{h + t + u = 12}}} Move back to the first equation



{{{2t-u + t + u = 12}}} Plug in {{{h=2t-u}}}



{{{3t = 12}}} Combine like terms.



{{{t=(12)/(3)}}} Divide both sides by {{{3}}} to isolate {{{t}}}.



{{{t=4}}} Reduce. So the tens digit is 4



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{{{h=2t-u}}} Go back to the previously isolated equation



{{{h=2(4)-u}}} Plug in {{{t=4}}}



{{{h=8-u}}} Multiply



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{{{(100u + 10t + h) - (100h + 10t + u) = 198}}} Move onto the second equation



{{{(100u + 10(4) + 8-u) - (100(8-u) + 10(4) + u) = 198}}} Plug in {{{h=8-u}}} and {{{t=4}}}



{{{(100u + 40 + 8-u) - (100(8-u) + 40 + u) = 198}}} Multiply



{{{100u + 40 + 8-u - 100(8-u) - 40 - u = 198}}} Distribute the negative.



{{{100u + 40 + 8-u - 800+100u - 40 - u = 198}}} Distribute.



{{{198u-792=198}}} Combine like terms on the left side.



{{{198u=198+792}}} Add {{{792}}} to both sides.



{{{198u=990}}} Combine like terms on the right side.



{{{u=(990)/(198)}}} Divide both sides by {{{198}}} to isolate {{{u}}}.



{{{u=5}}} Reduce. So the units (or ones) digit is 5



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{{{h=8-u}}} Go back to the isolated equation



{{{h=8-5}}} Plug in {{{u=5}}}



{{{h=3}}} Subtract. So the hundreds digit is 3



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Answer:


So the digits are {{{h=3}}}, {{{t=4}}}, and {{{u=5}}}



This means that the original number is 345




Note: I appreciate you showing your work.