Choice Bhoice C is the correct answer. This addition equation requires subtraction to isolate $x$.

1. Start with the equation: $x + 35 = 62$
2. Subtract 35 from both sides: $x = 62 - 35$
3. Calculate: $x = 27$
4. Verify: $27 + 35 = 62$ ✓

This reinforces the fundamental concept that subtraction undoes addition.

Choice Bhoice D is incorrect because this results from adding instead of subtracting: $62 + 35 = 97$. This is the opposite of what we need.

Choice Bhoice A is incorrect because this confuses the constant (35) with the solution. Seeing 35 in the equation doesn't mean $x = 35$.

Choice Bhoice C is incorrect because this is the negative of the correct answer. Perhaps from incorrectly calculating $35 - 62 = -27$ (reversing the subtraction order).