Step 1: Determine the operations represented by A, B, and C. We are given two equations: 1. $30 \text{ A } 10 \text{ B } 30 \text{ C } 10 = 37$ 2. $45 \text{ A } 15 \text{ B } 18 \text{ C } 9 = 58$ Let's test common mathematical operations. If we assume: A = Addition (+) B = Subtraction (-) C = Division (÷) Let's check the first equation: $$30 + 10 - 30 \div 10$$ Following the order of operations (BODMAS/PEMDAS): First, division: $30 \div 10 = 3$ Then, addition and subtraction from left to right: $30 + 10 - 3 = 40 - 3 = 37$ This matches the given result for the first equation. Now, let's check the second equation with the same operations: $$45 + 15 - 18 \div 9$$ First, division: $18 \div 9 = 2$ Then, addition and subtraction from left to right: $45 + 15 - 2 = 60 - 2 = 58$ This also matches the given result for the second equation. So, the operations are: A = + B = - C = ÷ Step 2: Apply the determined operations to the target expression. The target expression is: $64 \text{ A } 34 \text{ B } 50 \text{ C } 5 = ?$ Substitute the operations: $$64 + 34 - 50 \div 5$$ Step 3: Calculate the value of the expression. Following the order of operations: First, perform the division: $$50 \div 5 = 10$$ The expression becomes: $$64 + 34 - 10$$ Next, perform the addition: $$64 + 34 = 98$$ The expression becomes: $$98 - 10$$ Finally, perform the subtraction: $$98 - 10 = 88$$ The value of the expression is 88. Comparing with the given options: 1. 87 2. 88 3. 90 4. 80 The calculated value matches option 2. The final answer is $\boxed{\text{88}}$