Explanation:

- To find the correct value of \( y \), let's form two equations based on the given conditions.

- Equation 1: The weighted average of x and y is 37. Hence, \(\frac{5x + 7y}{12} = 37\).

- Equation 2: Another weighted average with a different order, \(\frac{7x + 5y}{12} = 35\).

- Solving these equations step-by-step, multiply both sides of each equation by 12 to eliminate the fraction.

$$

5x + 7y = 444

$$

$$

7x + 5y = 420

$$

- Solve these equations simultaneously by eliminating x or y.

Multiply the first equation by 7 and the second by 5:

$$

35x + 49y = 3108

$$

$$

35x + 25y = 2100

$$

- Subtract the second equation from the first:

$$

24y = 1008

$$

$$

y = 42

$$

- Therefore, ? Option 2: 42 is correct.

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