SOLUTION: I submitted this question a little earlier. This is the first time I have ever used this site. It is great; thank you! I just read how you like to see work. Anyway, I did not d

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Question 172652: I submitted this question a little earlier. This is the first time I have ever used this site. It is great; thank you! I just read how you like to see work. Anyway, I did not do that. So here is the question again: The sum of the three digits is 12. The tens digit exceeds the hundreds digit by the same amount that the units digit exceeds the tens digit. If the digits are reversed, the new number exceeds the original number by 198. Find the original number. Here is my work: H + T + U = 12. (100u + 10t + h) - (100H + 10T + u) = 198. The example in the textbook is simple. This is more complicated. I've been working at it for some time. I appreciate you help so much!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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%2Bh Add h to both sides.


t%2Bt=u%2Bh Add t to both sides.


t%2Bt-u=h Subtract u from both sides.


2t-u=h Combine like terms.


h=2t-u Rearrange the equation.


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h+%2B+t+%2B+u+=+12 Move back to the first equation


2t-u+%2B+t+%2B+u+=+12 Plug in h=2t-u


3t+=+12 Combine like terms.


t=%2812%29%2F%283%29 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%284%29-u Plug in t=4


h=8-u Multiply


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%28100u+%2B+10t+%2B+h%29+-+%28100h+%2B+10t+%2B+u%29+=+198 Move onto the second equation


%28100u+%2B+10%284%29+%2B+8-u%29+-+%28100%288-u%29+%2B+10%284%29+%2B+u%29+=+198 Plug in h=8-u and t=4


%28100u+%2B+40+%2B+8-u%29+-+%28100%288-u%29+%2B+40+%2B+u%29+=+198 Multiply


100u+%2B+40+%2B+8-u+-+100%288-u%29+-+40+-+u+=+198 Distribute the negative.


100u+%2B+40+%2B+8-u+-+800%2B100u+-+40+-+u+=+198 Distribute.


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


198u=198%2B792 Add 792 to both sides.


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


u=%28990%29%2F%28198%29 Divide both sides by 198 to isolate u.


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


--------------------------------------------

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.