# Math

posted by .

The letters A,B,and C represent three different digits. Determine the number ABC if ABC
+ ACB
----------
BCA

• Math -

What three different digits are represented by X,Y,Z in this addition problem?
XZY + XYZ = YZX

Just another perspective:

1--First, from the last column, we could have either Y + Z = X or Y + Z = 10 + X
2--From the second column, we could have either Y + Z = Z or Y + Z + 1 = 10 + Z
3--But we can't have (Y + Z) equaling both X and Z, so Y and Z must add up to more than 10.
3--Now we have Y + Z = 10 + X and Y + Z + 1 = 10 + Z or Y + Z = Z + 9.
4--Equating (Y + Z)'s, we get 10 + X = Z + 9 or X = Z - 1
5--Knowing that Y + Z exceeds 10, we can say 2X + 1 = Y
6--Substituting, we get 2X + 1 + Z = 10 + X or X = 9 - Z
7--Equating our expressions for X we get 9 - Z = Z - 1 or 2Z = 10 and Z = 5.

I thing the rest should fall out fairly easy for you.

## Similar Questions

1. ### Math

Twelve people serve on a board and are considering three alternatives: A, B, and C. The choices followed by vote is shown in following table. Determine the winner, if any, using a Borda count. (ABC) 2 (ACB) 4 (BAC) 2 (BCA) 1 (CAB) …
2. ### Math

Twelve people serve on a board and are considering three alternatives: A, B, and C. The choices followed by vote is shown in following table. Determine the winner, if any, using a Borda count. (ABC) 2 (ACB) 4 (BAC) 2 (BCA) 1 (CAB) …
3. ### simple GEOMETRY!!

In triangle ABC, ∠ABC=30∘,∠ACB=60∘. D is a point in triangle ABC such that DB and DC bisect angles ABC and ACB respectively. What is the measure (in degrees) of ∠BDC?
4. ### Geometry

ABC is an acute triangle with \angle BCA = 35 ^\circ. Denote the circumcenter of ABC as O and the orthocenter of ABC as H. If AO=AH, what is the value of \angle ABC (in degrees)?
5. ### maths

ABC is an acute triangle with \angle BCA = 35 ^\circ. Denote the circumcenter of ABC as O and the orthocenter of ABC as H. If AO=AH, what is the value of \angle ABC (in degrees)?
6. ### maths

ABC is an acute triangle with ∠BCA=35∘. Denote the circumcenter of ABC as O and the orthocenter of ABC as H. If AO=AH, what is the value of ∠ABC(in degrees)?
7. ### Maths

How many three digits numbers N=abc are there such that a≤b and c≤b?