rational models and independent variables

Question

Several families are going on a fishing trip and agree to divide the cost. It cost 5500.00 to rent the fishing boat. In addition to the rental fee adult and children pay fares that include bait and fishing rod. The cost depends on how many people are going on the fishing trip. The formula is c=80p+52*1+5500/P. C is cost for each adult will pay. P is the number of adults going on the trip with a total of 1 child. Define the variable for the number of adults going on the fishing trip use the variable to write the expression for the cost each adult will pay for the trip.

 

what is the cost for 133 adults and for 87 adults.

 

I am so confused on this.

 

Thank you

Answer 1

Shawna, what class is this for, anyway?

Because, what we are trying to do is to find the inverse of a function, but there are a few issues.

The equation, as you originally wrote it, requires an incredibly complicated process to solve it, including finding the roots of a derived polynomial, etc...

However, if c is the cost per adult, then the equation should be simple: c = 80 + (52+5500)/p = 80 + 5552/p.

If so, the inverse is simple: subtract 80 from both sides, take the multiplicative inverse of each side, then multiply both sides by 5552: 5552/(c-80) = p.

This is a rational function, we are switching the independent and dependent variables as we solve for the inverse, it makes a lot more sense, and it seems like something within reach of a reasonably basic college class.

So, given c as a function of p   c = f(p) = 80 + 5552/p, and solving for p = f(c) = 5552/(c-80), we have one answer, then plugging in our input values for p, we have c(87) = 143.82 and c(133) = 121.74.  That looks like everything requested in the problem.

Is this what we are looking for?

Otherwise, the formula you gave does not correspond to the very next sentence, that c is the cost per adult.  Neither does that formula correspond to a total cost, which would have a term "+5500", not a term "+5500/p".  The total cost (not the cost per adult) would be c = 80p + 52 + 5500, which immediately simplifies to c = 80p + 5552.

I am thinking it looks so complicated perhaps because something got copied wrong.  Speaking from experience, both as a student and as a math teacher helping students, it is difficult to overstate the trouble people have with problems just because the problem got copied wrong.  Might this be what happened here?

?  :)