Solve the math puzzle: A + B = 76, A - B = 38, find A ÷ B.

To solve the problem, we need to find the values of \( A \) and \( B \) using the given equations, and then compute \( A \div B \).

The given equations are:
1. \( A + B = 76 \)
2. \( A - B = 38 \)

Step 1: Solve for \( A \) and \( B \)

We can use the method of elimination or substitution. Here, we will use the elimination method.

#### Add the two equations:
\[
(A + B) + (A - B) = 76 + 38
\]
\[
A + B + A - B = 114
\]
\[
2A = 114
\]
\[
A = \frac{114}{2}
\]
\[
A = 57
\]

#### Substitute \( A = 57 \) into the first equation \( A + B = 76 \):
\[
57 + B = 76
\]
\[
B = 76 - 57
\]
\[
B = 19
\]

Step 2: Compute \( A \div B \)

Now that we have \( A = 57 \) and \( B = 19 \), we can find \( A \div B \):
\[
A \div B = \frac{A}{B} = \frac{57}{19}
\]
\[
\frac{57}{19} = 3
\]

Final Answer:

\[
\boxed{3}
\]