Final answer:
To solve the equation derived from the student's question, we first cleared the fractions by multiplying with a common multiple and then isolated the variable. The solution we found is that the number is 48, corresponding to option (d).
Step-by-step explanation:
The student's question reads: "Five-sixths of a number decreased by three is equal to five-eighths of a number increased by 7. What is the number?" We'll denote the number as 'x' and set up an equation based on the question: (5/6)x - 3 = (5/8)x + 7.
First, clear the denominators by finding a common multiple of 6 and 8, which is 24. Multiplying the entire equation by 24 to clear the fractions gives us 20x - 72 = 15x + 168.
To solve for 'x', move all terms involving 'x' to one side and the constant terms to the opposite side: 20x - 15x = 168 + 72, which simplifies to 5x = 240. Dividing both sides by 5 gives us x = 48.
Therefore, the number we are looking for is 48, which corresponds to option (d).