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

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) (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

Start with the third equation

Add to both sides.

Add to both sides.

Subtract from both sides.

Combine like terms.

Rearrange the equation.

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

Move back to the first equation

Plug in

Combine like terms.

Divide both sides by to isolate .

Reduce. So the tens digit is 4

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

Go back to the previously isolated equation

Plug in

Multiply

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

Move onto the second equation

Plug in and

Multiply

Distribute the negative.

Distribute.

Combine like terms on the left side.

Add to both sides.

Combine like terms on the right side.

Divide both sides by to isolate .

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

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

Go back to the isolated equation

Plug in

Subtract. So the hundreds digit is 3

===========================================================

Answer:

So the digits are , , and

This means that the original number is 345

Note: I appreciate you showing your work.
RELATED QUESTIONS
hello. here is my problem: "SOLVE: The difference if two consecutive odd positive... (answered by ankor@dixie-net.com)

I asked a question ten minutes ago and have since found the answer on this site. I cannot (answered by jim_thompson5910)

Hi tutors I submitted a few questions earlier and was wondering if it was possible to... (answered by duggie)

I am taking college Algebra for the first time and since math has always been my worst... (answered by yhtong)

Hello. This is my first time using this site. I hope I've submitted this question... (answered by scott8148)

I ALREADY ASKED THIS QUESTION, BUT IT GOT MESSED UP THE FIRST TIME I SUBMITTED. For... (answered by lynnlo,Alan3354)

Hello I submitted this problem earlier but, forgot the 2 in my email. Could I still have... (answered by josmiceli)

Hello! I have used this site Before and it was incredibly useful therefore I was... (answered by Boreal)

I asked this earlier. Thanks Ed for replying. I could npt get the site to open where I... (answered by edjones)