To solve the problem of how many students prefer Pepsi given that the ratio of Coke to Pepsi preferences is 5:7 and 84 students were surveyed, we can follow these steps:
1. Understand the Ratio: The ratio of students who prefer Coke to those who prefer Pepsi is 5:7. This means for every 5 students who prefer Coke, there are 7 students who prefer Pepsi.
2. Sum of Ratio Parts: Add the parts of the ratio to find the total number of parts. The ratio sum [tex]\( 5 + 7 = 12 \)[/tex].
3. Determine the Value of Each Part: Since there are 84 students surveyed and the total ratio is divided into 12 parts, each part represents [tex]\( \frac{84}{12} = 7 \)[/tex] students.
4. Calculate the Number of Students for Each Preference:
- Students who prefer Coke: [tex]\( 5 \times 7 = 35 \)[/tex] students.
- Students who prefer Pepsi: [tex]\( 7 \times 7 = 49 \)[/tex] students.
Since the question asks for the number of students who prefer Pepsi, the answer is:
c. 49
