Final answer:
To solve the equation provided by the student, one must set up and solve an algebraic equation using the given fractional relationships; however, the resulting answer of x = 126 does not match the available options, indicating a possible issue with the question's details or the provided answer choices.
Step-by-step explanation:
The student is asked to solve the equation: one-fourth of a number added to two-sevenths of it gives 135. Let's define the number as x. The equation can be written as (1/4)x + (2/7)x = 135. To solve for x, find a common denominator for the fractions, which is 28, and rewrite the equation as (7/28)x + (8/28)x = 135. Combine the terms to get (15/28)x = 135. Multiply both sides by (28/15) to isolate x, which gives x = 135 * (28/15). Simplifying gives x = 126. However, this is not one of the options provided, which suggests there may be a mistake in the original question or the answer choices. In a situation like this, it is important to recheck the calculations or clarify the question.