7. In a math competition, there are three problems: $A$, $B$, and $C$. Among the 39 participants, each person answered at least one question correctly. Among those who answered $A$ correctly, those who only answered $A$ are 5 more than those who answered other questions as well; among those who did not answer $A$ correctly, the number of people who answered $B$ is twice the number of people who answered $C$; it is also known that the number of people who only answered $A$ is equal to the sum of the number of people who only answered $B$ and the number of people who only answered $C$. Therefore, the maximum number of people who answered $A$ is $\qquad$
【Answer】 23
【Analysis】According to the problem, as shown in the following diagram: the number of people who only answered $A$ correctly is $3 b+a$, and the number of people who answered $A$ and other questions correctly is $3 b+a-5$. Therefore, we have: $3 b+a+3 b+a-5+3 b+2 a=39$.

Simplifying, we get $4 a+9 b=44$, solving which yields $\left\{\begin{array}{l}a=2 \\ b=4\end{array}\right.$ or $\left\{\begin{array}{l}a=11 \\ b=0\end{array}\right.$,
The number of people who answered $A$ correctly is $3 b+a+3 b+a-5=6 b+2 a-5$, with the maximum value being $6 \times 4+2 \times 2-5=23$ (people).