Find the values of $$A$$, $$B$$ and $$C$$ that fulfill the following sum: $$$\begin{eqnarray} & & 7 \ \ \ A \ \ \ 4 \\\\ &+ & \underline{1 \ \ \ 2 \ \ \ C} \\\\ & & B \ \ \ 6 \ \ \ 1 \end{eqnarray}$$$
where $$A$$, $$B$$ and $$C$$ are positive numbers.
See development and solution
Development:
First of all we write the sum as a table:
| $$7$$ | $$A$$ | $$4$$ |
| $$1$$ | $$2$$ | $$C$$ |
| $$B$$ | $$6$$ | $$1$$ |
In the last column, we have the sum $$$4+C=11$$$
as $$C$$ is said to be positive, the result is $$11$$, and $$C$$ should be $$7$$ so that the result is $$11$$.
We kept a $$1$$ so the second column becomes: $$$A+2+1=6 \rightarrow A+3=6$$$
then $$A$$ should be $$3$$ so that the result is $$6$$.
Finally, given that now we didn’t need any extra one: $$$7+1=B$$$
Therefore, $$B$$ should be $$8$$.
Solution:
$$A=3, \ B=8 \ C=7$$