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

Options

A. `36 xx 6 + 7 -:2 - 6 = 20`
B. `36 -: 6 + 3 xx 5 - 3 = 45 `
C. `36 + 6 - 3 xx 5 -: 3 = 24`
D. `36 - 6 + 3 xx 5 -: 3 = 74`

Explanation

To solve the problem, we need to interpret the symbols as follows:

- "+" stands for "division"
- "xx" stands for "addition"
- "-" stands for "multiplication"
- "-:" stands for "subtraction"

Now, we will evaluate each option step by step to find the correct equation.

### Step 1: Evaluate Option 1
**Equation:** 36 - 6 + 7 ÷ 2 - 6 = 20

**Interpretation:**
- 36 remains 36
- - (minus) becomes multiplication
- 6 remains 6
- + (plus) becomes division
- 7 remains 7
- ÷ (division) becomes subtraction
- 2 remains 2
- - (minus) becomes multiplication
- 6 remains 6

**Transformed Equation:**
36 * 6 ÷ 7 - 2 * 6

**Calculation:**
1. Perform multiplication:
- 36 * 6 = 216
2. Perform division:
- 216 ÷ 7 = 30.857 (approximately)
3. Perform multiplication:
- 2 * 6 = 12
4. Perform subtraction:
- 30.857 - 12 = 18.857 (approximately)

**Conclusion:** This does not equal 20. Option 1 is incorrect.

### Step 2: Evaluate Option 2
**Equation:** 36 ÷ 6 + 3 * 5 - 3 = 45

**Interpretation:**
- 36 remains 36
- ÷ (division) becomes subtraction
- 6 remains 6
- + (plus) becomes division
- 3 remains 3
- * (multiplication) becomes addition
- 5 remains 5
- - (minus) becomes multiplication
- 3 remains 3

**Transformed Equation:**
36 - 6 ÷ 3 + 5 * 3

**Calculation:**
1. Perform subtraction:
- 36 - 6 = 30
2. Perform division:
- 30 ÷ 3 = 10
3. Perform addition:
- 5 * 3 = 15
4. Perform addition:
- 10 + 15 = 25

**Conclusion:** This does not equal 45. Option 2 is incorrect.

### Step 3: Evaluate Option 3
**Equation:** 36 + 6 - 3 * 5 ÷ 3 = 24

**Interpretation:**
- 36 remains 36
- + (plus) becomes division
- 6 remains 6
- - (minus) becomes multiplication
- 3 remains 3
- * (multiplication) becomes addition
- 5 remains 5
- ÷ (division) becomes subtraction
- 3 remains 3

**Transformed Equation:**
36 ÷ 6 * 3 + 5 - 3

**Calculation:**
1. Perform division:
- 36 ÷ 6 = 6
2. Perform multiplication:
- 6 * 3 = 18
3. Perform addition:
- 18 + 5 = 23
4. Perform subtraction:
- 23 - 3 = 20

**Conclusion:** This does not equal 24. Option 3 is incorrect.

### Step 4: Evaluate Option 4
**Equation:** 36 - 6 + 3 * 5 ÷ 3 = 74

**Interpretation:**
- 36 remains 36
- - (minus) becomes multiplication
- 6 remains 6
- + (plus) becomes division
- 3 remains 3
- * (multiplication) becomes addition
- 5 remains 5
- ÷ (division) becomes subtraction
- 3 remains 3

**Transformed Equation:**
36 * 6 ÷ 3 + 5 - 3

**Calculation:**
1. Perform multiplication:
- 36 * 6 = 216
2. Perform division:
- 216 ÷ 3 = 72
3. Perform addition:
- 72 + 5 = 77
4. Perform subtraction:
- 77 - 3 = 74

**Conclusion:** This equals 74. Option 4 is correct.

### Final Answer:
The correct equation is **Option 4**.