Answer:
- independent: number of persons
- dependent: charges
Explanation:
The scenario describes charges as being dependent on the number of persons. That means the independent variable is the number of persons, and the dependent variable is the total charge.
(When we say "A depends on B", that automatically defines A as being the dependent variable, and B the independent variable.)
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Additional comment
Perhaps you also want to know the relationship between the charges c and the number of persons p. That will be ...
c = 7.80p +19.00
You know the rate per person from the fact that adding 10 people to the party raises the cost by $78. Then the 10-person charge includes a fixed fee of $97 -78 = $19.