In a coded arithmetic system, the meanings of the operators are changed as follows: the symbol plus (+) means minus (-), the symbol minus (-) means multiplication (x), the symbol division (÷) means plus (+), and the symbol x means division (÷). Using this coding, what is the value of the expression 15 - 3 + 10 x 5 ÷ 5?

Introduction / Context:
This problem again changes the meanings of all four basic arithmetic operators. To solve it, we must first translate the given coded expression to a normal arithmetic expression using the provided mapping. After that, we compute the numerical value using ordinary precedence rules. The question checks your ability to keep track of operator meanings and to perform multi step calculations accurately.

Given Data / Assumptions:

• + means minus (-). span style="display:block;">• - means multiplication (x). • ÷ means plus (+). • x means division (÷). • Expression: 15 - 3 + 10 x 5 ÷ 5.

Concept / Approach:
We decode the expression by substituting each symbol with its actual operation. Then we apply the established arithmetic rule that multiplication and division have higher precedence than addition and subtraction. Finally, we perform the operations step by step. It is very useful to rewrite the entire expression in decoded form before starting the calculation to avoid mixing coded and real meanings in your mind.

Step-by-Step Solution:
Step 1: Start with 15 - 3 + 10 x 5 ÷ 5. Step 2: Decode - as multiplication, so 15 - 3 becomes 15 x 3. Step 3: Decode + as minus, so + 10 becomes − 10. Step 4: Decode x as division, so 10 x 5 becomes 10 ÷ 5. Step 5: Decode ÷ as plus, so ÷ 5 becomes + 5. Step 6: Putting all replacements together, the decoded expression is 15 x 3 − 10 ÷ 5 + 5. Step 7: Apply precedence. First compute the multiplication and division: 15 x 3 = 45. Step 8: Compute 10 ÷ 5 = 2. Step 9: Now the expression becomes 45 − 2 + 5. Step 10: Evaluate from left to right: 45 − 2 = 43. Step 11: Finally 43 + 5 = 48.

Verification / Alternative check:
As a verification, perform the arithmetic again quickly: 15 times 3 is 45, 10 divided by 5 is 2, then 45 minus 2 plus 5 equals 43 plus 5 which is 48. The sequence is straightforward once decoded, and no alternative interpretation of the mapping is consistent with the given statement, so 48 is confirmed as the correct result.

Why Other Options Are Wrong:
Option 52 would require a final addition result of 9 instead of 5, which does not match the decoded expression. Option 22 is far too small and must result from major decoding or arithmetic errors. Option 5 ignores the large contribution from the multiplication 15 x 3 and therefore cannot be correct. Option 18 also fails to reflect the correct combination of the intermediate results 45 and 2.

Common Pitfalls:
A common mistake is to treat the operators with their usual meanings and ignore the coding, which leads to a completely different value. Another error is to forget that multiplication and division must be done before subtraction and addition after decoding. Rewriting the entire decoded expression and underlining the high precedence operations is a practical strategy to avoid these traps.

Final Answer:
After decoding and evaluating step by step, the value of 15 - 3 + 10 x 5 ÷ 5 under the given operator scheme is 48.