Total age of A and B is 12 years more than the total age of B and C.By how many years is C younger than A?

1. Break Down the Problem

• Let the ages of A, B, and C be represented as $A$, $B$, and $C$ respectively.
• According to the problem, we have the equation: $A + B = (B + C) + 12$

2. Relevant Concepts

• Rearranging the equation will help to isolate the variable we are interested in, which is the relationship between A and C.

3. Analysis and Detail

• Start with the equation: $A + B = B + C + 12$
• Subtract $B$ from both sides: $A = C + 12$
• This shows us that A is 12 years older than C. Therefore, to find how many years C is younger than A, we can express it as: $A - C = 12$

4. Verify and Summarize

• We verified that the relationship holds through the rearrangement of terms.
• The findings indicate that C is 12 years younger than A.

Final Answer

C is 12 years younger than A.