Challenge yourself with math puzzles on a tablet screen.

Problem Description:

The task is to solve for the value of \( \frac{A}{B} \) given the following equations:
1. \( A + B = 60 \)
2. \( A - B = 40 \)

Solution Approach:

To solve for \( \frac{A}{B} \), we need to determine the values of \( A \) and \( B \) first. We can do this by solving the system of linear equations using either substitution or elimination. Here, we will use the elimination method.

#### Step 1: Write down the equations
We have:
\[
A + B = 60 \quad \text{(Equation 1)}
\]
\[
A - B = 40 \quad \text{(Equation 2)}
\]

#### Step 2: Add the two equations
Adding Equation 1 and Equation 2 eliminates \( B \):
\[
(A + B) + (A - B) = 60 + 40
\]
\[
A + B + A - B = 100
\]
\[
2A = 100
\]
\[
A = 50
\]

#### Step 3: Substitute \( A = 50 \) into one of the original equations
Substitute \( A = 50 \) into Equation 1:
\[
50 + B = 60
\]
\[
B = 60 - 50
\]
\[
B = 10
\]

#### Step 4: Calculate \( \frac{A}{B} \)
Now that we have \( A = 50 \) and \( B = 10 \), we can find \( \frac{A}{B} \):
\[
\frac{A}{B} = \frac{50}{10} = 5
\]

Final Answer:

\[
\boxed{5}
\]