In each of the following questions if the interchanges are made in signs and numbers, which one of the four equations would be correct?
Given interchanges: Signs: `-:` and `+` and numbers 9 and 3

Options

A. `3 + 9 -: 4 = 8`
B. `3-:3 + 9 = 13`
C. `3+ 9 -: 2 = 5`
D. `3+ 9-:9 = 2`

Explanation

To solve the problem, we need to interchange the signs and numbers as specified. The interchanges are:

- Signs: `-` becomes `+` and `+` becomes `-`
- Numbers: `9` becomes `3` and `3` becomes `9`

Let's analyze each option step by step.

### Option 1:
**Original Equation:** \(3 + 9 \div 4 = 8\)

1. Interchange `3` with `9`:
- New equation: \(9 + 3 \div 4 = 8\)

2. Interchange `+` with `-`:
- New equation: \(9 - 3 \div 4 = 8\)

3. Now calculate \(9 - 3 \div 4\):
- First, perform the division: \(3 \div 4 = 0.75\)
- Then, subtract: \(9 - 0.75 = 8.25\)

This does not equal \(8\), so **Option 1 is incorrect**.

### Option 2:
**Original Equation:** \(3 \div 3 + 9 = 13\)

1. Interchange `3` with `9`:
- New equation: \(9 \div 9 + 3 = 13\)

2. Interchange `+` with `-`:
- New equation: \(9 \div 9 - 3 = 13\)

3. Now calculate \(9 \div 9 - 3\):
- First, perform the division: \(9 \div 9 = 1\)
- Then, subtract: \(1 - 3 = -2\)

This does not equal \(13\), so **Option 2 is incorrect**.

### Option 3:
**Original Equation:** \(3 + 9 \div 2 = 5\)

1. Interchange `3` with `9`:
- New equation: \(9 + 3 \div 2 = 5\)

2. Interchange `+` with `-`:
- New equation: \(9 - 3 \div 2 = 5\)

3. Now calculate \(9 - 3 \div 2\):
- First, perform the division: \(3 \div 2 = 1.5\)
- Then, subtract: \(9 - 1.5 = 7.5\)

This does not equal \(5\), so **Option 3 is incorrect**.

### Option 4:
**Original Equation:** \(3 + 9 \div 9 = 2\)

1. Interchange `3` with `9`:
- New equation: \(9 + 3 \div 9 = 2\)

2. Interchange `+` with `-`:
- New equation: \(9 - 3 \div 9 = 2\)

3. Now calculate \(9 - 3 \div 9\):
- First, perform the division: \(3 \div 9 = \frac{1}{3}\)
- Then, subtract: \(9 - \frac{1}{3} = 8.67\)

This does not equal \(2\), so **Option 4 is incorrect**.

### Conclusion:
After checking all options, it appears there was an error in the analysis of Option 3. Let's re-evaluate it:

For Option 3:
**Original Equation:** \(3 + 9 \div 2 = 5\)

1. Interchange `3` with `9`:
- New equation: \(9 + 3 \div 2 = 5\)

2. Interchange `+` with `-`:
- New equation: \(9 - 3 \div 2 = 5\)

3. Now calculate \(9 - 3 \div 2\):
- First, perform the division: \(3 \div 2 = 1.5\)
- Then, subtract: \(9 - 1.5 = 7.5\)

This does not equal \(5\), so **Option 3 is incorrect**.

### Final Answer:
None of the options provided are correct after the interchanges.