If the symbols represent the following operations: 'A' stands for division (÷), 'B' stands for multiplication (×), 'C' stands for addition (+), and 'D' stands for subtraction (−), what is the value of the expression?

$$55 \ B \ 5 \ D \ 13 \ B \ 2 \ C \ 14 \ A \ 7 \ D \ 15 \ B \ 5 \ C \ 102 \ A \ 2 \ C \ 15 = ?$$

Question

If the symbols represent the following operations: 'A' stands for division (÷), 'B' stands for multiplication (×), 'C' stands for addition (+), and 'D' stands for subtraction (−), what is the value of the expression?

$$55 \ B \ 5 \ D \ 13 \ B \ 2 \ C \ 14 \ A \ 7 \ D \ 15 \ B \ 5 \ C \ 102 \ A \ 2 \ C \ 15 = ?$$

Accepted Answer

**Solution:**

1. First, substitute the given symbols with their respective operations:
   - A = ÷
   - B = ×
   - C = +
   - D = −

So, the expression becomes:
   $$55 	imes 5 - 13 	imes 2 + 14 \div 7 - 15 	imes 5 + 102 \div 2 + 15$$

2. According to BODMAS, perform multiplication and division from left to right:
   - $$55 	imes 5 = 275$$
   - $$13 	imes 2 = 26$$
   - $$14 \div 7 = 2$$
   - $$15 	imes 5 = 75$$
   - $$102 \div 2 = 51$$

Now the expression is:
   $$275 - 26 + 2 - 75 + 51 + 15$$

3. Perform addition and subtraction from left to right:
   - $$275 - 26 = 249$$
   - $$249 + 2 = 251$$
   - $$251 - 75 = 176$$
   - $$176 + 51 = 227$$
   - $$227 + 15 = 242$$

**Answer:** $242$

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