Step 1: Determine the operations for A, B, and C. We are given two equations: 1) $13 \text{ A } 14 \text{ B } 15 \text{ C } 20 = 243$ 2) $15 \text{ A } 10 \text{ B } 8 \text{ C } 9 = 104$ Let's test common arithmetic operations. If we assume A is addition (+), B is multiplication (×), and C is addition (+), let's check if these operations satisfy both equations. For equation 1: $$13 + 14 \times 15 + 20$$ Following the order of operations (BODMAS/PEMDAS), multiplication is performed first: $$13 + (14 \times 15) + 20$$ $$13 + 210 + 20$$ $$223 + 20 = 243$$ This matches the given result. For equation 2: $$15 + 10 \times 8 + 9$$ Following the order of operations: $$15 + (10 \times 8) + 9$$ $$15 + 80 + 9$$ $$95 + 9 = 104$$ This also matches the given result. Thus, the operations are: A = + (addition) B = × (multiplication) C = + (addition) Step 2: Apply the identified operations to the target expression. The expression to evaluate is: $$45 \text{ A } 10 \text{ B } 18 \text{ C } 50$$ Substitute the operations: $$45 + 10 \times 18 + 50$$ Step 3: Calculate the value of the expression. Following the order of operations, perform multiplication first: $$10 \times 18 = 180$$ Now substitute this value back into the expression: $$45 + 180 + 50$$ Perform the additions from left to right: $$45 + 180 = 225$$ $$225 + 50 = 275$$ The value of the expression is 275. Comparing this with the given options: 1. 265 2. 280 3. 145 4. 275 The calculated value matches option 4. The final answer is $\boxed{\text{275}}$.