Question

The attendence at a water park varies directly as the temperature and invesely as the number of days of rain during the month. If during a given month, the average daily temperature is 88 degrees F and it rains 8days, the total attendance for the month is 3200 people. What attendence should the park expect if it rains 12 days and the average daily temperature is 92 degrees F?

Answer 1

Let A be attendance, t the temperature and n the number of days. Then,
A
`\alpha`
`(t)/(n)`
A=k
`(t)/(n)`
Where k is a constant of proportionality;
If A=3200, T=88 and n=8, then k,
3200=
`(88k)/(8)`
3200=11k
k=
`(3200)/(11)`
Rewriting the equation and replacing the value of k,
A=
`(3200t)/(11n)`
When t=92 and n=12
The A=
`(3200*92)/(11*12)`
A=
`(294400)/(132)`
A= 2231