Let's analyze the equation given in the problem: [tex]\( C = 6x + 6.5y \)[/tex].
1. Understanding the Components:
- [tex]\( x \)[/tex]: Represents the number of 7th graders.
- [tex]\( y \)[/tex]: Represents the number of 8th graders.
- The number 6: Indicates the cost per 7th grader.
- The number 6.5: Indicates the cost per 8th grader.
2. Breaking Down the Equation:
- The term [tex]\( 6x \)[/tex]: This part of the equation calculates the total cost for all the 7th graders going on the field trip. Since the cost per 7th grader is \[tex]$6, for \( x \) 7th graders, the total cost would be \( 6 \times x \).
- The term \( 6.5y \): Similarly, this part of the equation calculates the total cost for all the 8th graders. Since the cost per 8th grader is \$[/tex]6.50, for [tex]\( y \)[/tex] 8th graders, the total cost would be [tex]\( 6.5 \times y \)[/tex].
- By adding these two results, [tex]\( 6x \)[/tex] and [tex]\( 6.5y \)[/tex], we get the overall total cost for both 7th and 8th graders attending the field trip.
3. Interpreting [tex]\( C \)[/tex]:
- [tex]\( C \)[/tex] is the result of adding the total cost for 7th graders ([tex]\( 6x \)[/tex]) and the total cost for 8th graders ([tex]\( 6.5y \)[/tex]). Therefore, [tex]\( C \)[/tex] represents the total cost of taking all the students (both 7th and 8th graders) on the field trip.
4. Conclusion:
- Among the options provided, the correct interpretation matches option D: "the total cost of taking all the students on the field trip."
So, the variable [tex]\( C \)[/tex] represents the total cost of taking all the students on the field trip, making the correct answer:
D. the total cost of taking all the students on the field trip
