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QUESTION: Hello:

Can you explain why students are directly or indirectly proportional to days in the following?

The dorm charges \$6300 for 35 students for 24 days. In how many days will the dorm charges be \$3375 for 25 students?

I think the dorm charges are directly proportional to days because when the number of days increases so would the charges, but I cannot determine whether or not the students are directly or indirectly proportional to days.

Can you explain why students are directly or indirectly proportional to days?

You do not need to solve for the answer. I think it is 18 days.

ANSWER: Days and students are independent variables . Neither directly nor inversely proportional.

Total dorm charges are directly proportional to the product of students and days.

18 is correct

---------- FOLLOW-UP ----------

QUESTION: Hello:

I want to thank you for your reply.  I am still somewhat confused.

If days and students are independent variables, neither directly nor inversely proportional, what does this indicate?

And, total dorm charges are directly proportional to the product of students and days. Can you explain this as well?

I thank you for your assistance.

It means neither one determines the other.  If you are told one , you can't figure out the other. For example , a person's height and age are independent variables. If I tell you that a man is 30 years old , there's no way to tell the man's height just based on that . Similarly , if I tell you a man's height is 6 feet , you can't tell his age.The number of students and the number of days are independent in this same way

From the fact that 35 students for 24 days costs
\$6300 , you can calculate that the cost per day for each student is \$7.50

Thus , if there are s students staying for d days the charges will be c = (7.50)(s)(d)
So total charges c is directly proportional to the product of the number of days and the number of students,  with constant of proportionality 7.50

I hope this helps
Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment Thanks for the reply and clarification!

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#### Socrates

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I can answer any questions from the standard four semester Calulus sequence. Derivatives, partial derivatives, chain rule, single and multiple integrals, change of variable, sequences and series, vector integration (Green`s Theorem, Stokes, and Gauss) and applications. Pre-Calculus, Linear Algebra and Finite Math questions are also welcome.

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