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Mr. Anderson is taking a group of junior high school students (7th and 8th graders) on a field trip to a local observatory. The cost for 7th graders is \[tex]$6, and the cost for 8th graders is \$[/tex]6.50. In the equation [tex]C=6x + 6.5y[/tex], what does the variable [tex]\(C\)[/tex] represent?

A. the total number of 7th graders attending the field trip

B. the total number of students attending the field trip

C. the total cost of taking the 8th graders on the field trip

D. the total cost of taking all the students on the field trip

Sagot :

GinnyAnsweridn
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
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