Question

If a, b, and c are digits for which the following holds, then a +b+c= 9 a 1-7 2 b= c 8 2a+b+c=

Answer 1

Answer:

11

Explanation:

Given the difference:

$\begin{gathered} \; \; 9\text{ a 1} \\ -7\text{ 2 b} \\ ---- \\ \; \; c\text{ 8 2} \end{gathered}$$\begin{gathered} 11-9=2 \\ \text{Therefore, b=9} \end{gathered}$$\begin{gathered} 10-2=8 \\ 10+1=11 \\ \text{Therefore, a=1} \end{gathered}$

Lastly:

$\begin{gathered} (9-1)-7=1 \\ \text{Therefore: c=1} \end{gathered}$

We then have:

$\begin{gathered} \; \; 9\text{ 1 1} \\ -7\text{ 2 }9 \\ ---- \\ \; \; 1\text{ 8 2} \end{gathered}$

Therefore:

a+b+c=9+1+1=11