Sunday

December 21, 2014

December 21, 2014

Posted by **Devin** on Monday, February 14, 2011 at 11:19am.

+ ACB

----------

BCA

- Math -
**tchrwill**, Monday, February 14, 2011 at 12:35pmWhat 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.

**Answer this Question**

**Related Questions**

5th grade math - In the multiplication problem at the right different letters ...

Math - Twelve people serve on a board and are considering three alternatives: A...

Math - Twelve people serve on a board and are considering three alternatives: A...

simple GEOMETRY!! - In triangle ABC, ∠ABC=30∘,∠ACB=60∘. ...

maths - ABC is an acute triangle with ∠BCA=35∘. Denote the ...

maths - ABC is an acute triangle with \angle BCA = 35 ^\circ. Denote the ...

Geometry - ABC is an acute triangle with \angle BCA = 35 ^\circ. Denote the ...

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

math - in triangle ABC, AB = BC and ABC = 42. find ACB

Calculus - In the multiplication shown below, the digits have been replaced by ...