Proportions

[caaja]

In the summer, the monthly attendance at Six Flag’s water park varies directly as the temperature and inversely as the number of days of rain during the month. If during a given month the average daily temperature is 88°F and it rains 8 days, the total attendance for the month is 3,200. What attendance should we expect for a month (of the same length) if it rains 12 days and the average daily temperature is 92°F?

I am completely confused on this one. Here is what I know -

Inversely Proportional Formula is y=k/x
Directly Proportional Formula is y=kx

So here's what I tried....

The temperature represented as T (in Fahrenheit)
The number of rainy days represented as R
The total attendance for the month represented as A


88 = k(92)
k = 88/92
k = 0.96 (rounded to nearest hundredth)

8 = k/12
k = 8(12)
k = 96
...I don't even know if that is how I am supposed to start the problem.
Thanks for your help!

 

[mmm4444bot]

The two k's (from both variations) will combine into a single constant. You need to find it.

Direct variation with T means that T is in the numerator; inverse variation with R means that R is in the denominator.

Let's call the combined constants of variation big K.

A = K * T/R

Use the given A, T, and R to find K.

Then use the second given T and R with K to answer the question.

Does that help ?

 

[caaja]

Wow, Thank you so much! I think I got it

I did.....

3200 = k * 88/8
32000 = k * 11
k = 290.90

A = 290.90 * 92/12
A = 2228.29

So the attendance would be 2228 people because you cant have 29% of a person right?

 

[mmm4444bot]

Check your rounding, or carry more digits with 290.9.

I get 2230 people.

 

[caaja]

Oh ok, I did it again and got the same.

You just taught me how to do that problem completely. Thanks!!!!!! :mrgreen: