Discussion
What would be the highest value of A?
\(\begin{array}{r} 4A2\\ 7B8\\ +\ 3C2\\ \hline 1472\end{array}\)
Answer: D
The highest value of A is 6.
The units column is 2 + 8 + 2 = 12, so 2 is written and 1 is carried. In the tens column A + B + C + 1 must give 7 with no carry, because the hundreds column 4 + 7 + 3 = 14 needs no extra carry to make 14. So A + B + C = 6.
\[ A+B+C=6 \Rightarrow A_{max}=6\ (B=C=0) \]
A larger digit is not possible, so 3, 4 and 5 are not the highest.
Since A, B and C are digits and the tens column sum is 6 plus the carry from the units, the largest A is found by making B and C as small as possible, namely 0. Then A = 6 and the sum 462 + 708 + 302 = 1472 checks out.
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