Some equations are solved according to a certain coding pattern. For example, 4 x 5 x 8 is written as 584 and 7 x 3 x 9 is written as 397. Using the same pattern, what is the code for 9 x 7 x 3?

Introduction / Context:
This question uses a simple rearrangement code applied to three numbers. The expressions 4 x 5 x 8 and 7 x 3 x 9 are not being evaluated arithmetically; instead, the numbers are being rearranged to form a three digit code. Our task is to identify this rearrangement pattern and apply it to the numbers 9, 7 and 3. The problem tests pattern recognition more than numerical calculation.

Given Data / Assumptions:

• 4 x 5 x 8 is coded as 584.
• 7 x 3 x 9 is coded as 397.
• The symbol x here is just a separator, not actual multiplication.
• The same rearrangement rule applies to all three number expressions.
• We must find the code for 9 x 7 x 3.

Concept / Approach:
Instead of computing products, we treat the three numbers as digits a, b and c. We then compare the given expressions and their codes digit by digit. For 4 x 5 x 8, the numbers are a = 4, b = 5, c = 8, and the code is 584. For 7 x 3 x 9, a = 7, b = 3, c = 9, and the code is 397. Observing these pairs suggests that the code is formed by placing the middle number first, the last number second and the first number third: (b, c, a). Once this rearrangement is identified, we simply apply it to 9, 7 and 3.

Step-by-Step Solution:
Step 1: For 4 x 5 x 8, note that the numbers are 4, 5 and 8. Step 2: The code 584 has digits 5, 8 and 4. This is the sequence middle, last, first. Step 3: For 7 x 3 x 9, the numbers are 7, 3 and 9. Step 4: The code 397 has digits 3, 9 and 7. Again, this is middle, last, first. Step 5: Conclude that the rule is: if the three numbers are a, b and c, the code is b c a. Step 6: Apply this to 9 x 7 x 3, where a = 9, b = 7, c = 3. Step 7: Arrange them as middle, last, first: 7, 3, 9. Step 8: Combine the digits to form the code 739.

Verification / Alternative check:
Checking the two examples again confirms that the pattern b c a is consistently used. There is no arithmetic involved and no other obvious rearrangement that would fit both 584 and 397 so neatly. Applying this rule to 9 x 7 x 3 gives 739, and among the options, only 739 matches this pattern. Thus the answer is unique and consistent with the given coding system.

Why Other Options Are Wrong:
Option 397 is the code for 7 x 3 x 9 and does not correspond to 9 x 7 x 3. Option 793 would be the arrangement c a b, and 973 would be a c b, neither of which follows the b c a pattern demonstrated in the examples. Option 937 similarly rearranges the digits in an unsupported order. Only 739 preserves the middle, last, first order required by the code.

Common Pitfalls:
Some students mistakenly try to multiply the numbers, since the symbol x is often used for multiplication, and then attempt to extract digits from the product. This leads away from the actual pattern, which is purely positional. Others may guess a reversal (c b a) or keep the original order (a b c) without carefully checking against the examples. Always compare all given codes and look for the simplest consistent rearrangement before assuming any arithmetic is involved.

Final Answer:
Using the same rearrangement pattern as in the examples, the code for 9 x 7 x 3 is 739.