If `xx` means 'addition', - means 'division', `-:` means 'subtraction' and + means 'multiplication', then which of the following equations is correct?

Options

A. `16 xx 5 -: 10 xx 4 = 19`
B. `16 + 5 -: 10 xx 4 -3 = 9`
C. `16 + 5 - 10 xx 4 -: 3 = 9`
D. `16 - 5 xx 10 -: 4 + 3 = 12`

Explanation

To solve the problem, we need to interpret the operations according to the given meanings:

1. **xx means addition (+)**
2. **- means division (/)**
3. **-: means subtraction (-)**
4. **+ means multiplication (×)**

Now, let's analyze each option step by step.

### Step-by-Step Solution

**Option 1: 16 xx 5 - 10 xx 4 = 19**

1. Replace the operations:
- 16 xx 5 becomes 16 + 5
- - becomes /
- 10 xx 4 becomes 10 + 4

Thus, the equation becomes:
\[ 16 + 5 / 10 + 4 \]

2. According to BODMAS/BIDMAS rules, we perform division first:
- \(5 / 10 = 0.5\)

3. Now substitute back:
\[ 16 + 0.5 + 4 \]

4. Perform the addition:
- \(16 + 0.5 = 16.5\)
- \(16.5 + 4 = 20.5\)

5. The left side equals 20.5, which is not equal to 19.
**Conclusion: Option 1 is incorrect.**

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**Option 2: 16 + 5 - 10 xx 4 - 3 = 9**

1. Replace the operations:
- 16 + 5 becomes 16 × 5
- - becomes /
- 10 xx 4 becomes 10 + 4
- -3 remains -3

Thus, the equation becomes:
\[ 16 × 5 / 10 + 4 - 3 \]

2. Perform the operations according to BODMAS:
- First, calculate \(16 × 5 = 80\)
- Then, calculate \(80 / 10 = 8\)
- Next, calculate \(8 + 4 = 12\)
- Finally, calculate \(12 - 3 = 9\)

3. The left side equals 9, which is equal to the right side.
**Conclusion: Option 2 is correct.**

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**Option 3: 16 + 5 - 10 xx 4 - 3 = 9**

1. Replace the operations:
- 16 + 5 becomes 16 × 5
- - becomes /
- 10 xx 4 becomes 10 + 4
- -3 remains -3

Thus, the equation becomes:
\[ 16 × 5 / 10 + 4 - 3 \]

2. Perform the operations according to BODMAS:
- First, calculate \(16 × 5 = 80\)
- Then, calculate \(80 / 10 = 8\)
- Next, calculate \(8 + 4 = 12\)
- Finally, calculate \(12 - 3 = 9\)

3. The left side equals 9, which is equal to the right side.
**Conclusion: Option 3 is also correct.**

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**Option 4: 16 + 5 - 10 xx 4 = 19**

1. Replace the operations:
- 16 + 5 becomes 16 × 5
- - becomes /
- 10 xx 4 becomes 10 + 4

Thus, the equation becomes:
\[ 16 × 5 / 10 + 4 \]

2. Perform the operations according to BODMAS:
- First, calculate \(16 × 5 = 80\)
- Then, calculate \(80 / 10 = 8\)
- Next, calculate \(8 + 4 = 12\)

3. The left side equals 12, which is not equal to 19.
**Conclusion: Option 4 is incorrect.**

### Final Answer
The correct options are **Option 2 and Option 3**.

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