20 Tricky But Fun Grade-School Math Questions - Hard Math Problems - Free Printable

Problem Analysis:

We are given two equations involving variables \( A \) and \( B \):
1. \( A + B = 76 \)
2. \( A - B = 38 \)

We need to find the value of \( A \div B \).

Step-by-Step Solution:

#### Step 1: Solve for \( A \) and \( B \)
We have a system of linear equations:
\[
\begin{cases}
A + B = 76 \\
A - B = 38
\end{cases}
\]

To solve for \( A \) and \( B \), we can add the two equations together to eliminate \( B \):
\[
(A + B) + (A - B) = 76 + 38
\]
\[
2A = 114
\]
\[
A = \frac{114}{2} = 57
\]

Now that we have \( A = 57 \), we can substitute this value back into one of the original equations to solve for \( B \). Using \( A + B = 76 \):
\[
57 + B = 76
\]
\[
B = 76 - 57 = 19
\]

So, we have:
\[
A = 57 \quad \text{and} \quad B = 19
\]

#### Step 2: Calculate \( A \div B \)
Now that we know \( A = 57 \) and \( B = 19 \), we can compute \( A \div B \):
\[
A \div B = \frac{A}{B} = \frac{57}{19}
\]

Simplify the fraction:
\[
\frac{57}{19} = 3
\]

Final Answer:

\[
\boxed{3}
\]