Solve the fruit math puzzle: What is the value of one banana plus one plum?

This is a classic fruit puzzle where we need to determine the value of each fruit and then solve for the final equation. Let's break it down step by step.

Step 1: Assign variables to the fruits

- Let the value of an apple be \( A \).
- Let the value of a banana bunch (two bananas) be \( B \).
- Let the value of a plum be \( P \).

Step 2: Translate the equations from the image

The image provides three equations:
1. \( A + A + A = 120 \)
2. \( A + B + B = 100 \)
3. \( B + P + A = 105 \)

We need to find the value of \( B + P \) in the final equation.

Step 3: Solve the first equation

From the first equation:
\[ A + A + A = 120 \]
\[ 3A = 120 \]
\[ A = \frac{120}{3} \]
\[ A = 40 \]

So, the value of an apple (\( A \)) is 40.

Step 4: Solve the second equation

Substitute \( A = 40 \) into the second equation:
\[ A + B + B = 100 \]
\[ 40 + 2B = 100 \]
\[ 2B = 100 - 40 \]
\[ 2B = 60 \]
\[ B = \frac{60}{2} \]
\[ B = 30 \]

So, the value of a banana bunch (\( B \)) is 30.

Step 5: Solve the third equation

Substitute \( A = 40 \) and \( B = 30 \) into the third equation:
\[ B + P + A = 105 \]
\[ 30 + P + 40 = 105 \]
\[ 70 + P = 105 \]
\[ P = 105 - 70 \]
\[ P = 35 \]

So, the value of a plum (\( P \)) is 35.

Step 6: Solve the final equation

The final equation asks for the value of:
\[ B + P \]

We already know:
- \( B = 30 \)
- \( P = 35 \)

So:
\[ B + P = 30 + 35 \]
\[ B + P = 65 \]

Final Answer:

\[
\boxed{65}
\]