A local club is arranging a charter flight to Miami. The cost of the trip is $225.00 each for 75 passengers, with a refund of $5.00 per passenger for each passenger in excess of 75. How many passengers must take the flight to produce revenue of $16,000.00?
No. of passengers = 75+x
Revenue from each passenger = 225-5x
= (75+x)(22-5x)
= 16 875 - 375x + 225x - 5x^2
How do I use this equation to find the number of passengers needed to make $16,000.00?
huh? Just solve
(75+x)(225-5x) = 16000
x = 5
so, ...
To find the number of passengers needed to make $16,000.00 in revenue, you need to set up an equation and solve for 'x', which represents the number of additional passengers.
The equation you have already set up is:
Revenue from each passenger = (75+x)(22-5x)
To find the total revenue, you need to multiply the number of passengers by the revenue from each passenger. So the equation for total revenue is:
Total Revenue = (75+x)(225-5x)
Now, you can set up another equation using the given information that the revenue should be $16,000.00:
16,000 = (75+x)(225-5x)
To solve this equation, you can start by expanding and simplifying:
16,000 = 16,875 - 375x + 225x - 5x^2
0 = 16,875 - 375x + 225x - 5x^2 - 16,000
0 = -5x^2 - 150x + 875
Now, you can rearrange the equation to be in the form of a quadratic equation:
5x^2 + 150x - 875 = 0
Next, you can solve this quadratic equation by factoring, using the quadratic formula, or by graphing. Once you solve for 'x', you will get the number of additional passengers needed to make $16,000.00 in revenue.
Note: It's important to note that you need to round the solution to a whole number since it represents the number of passengers. If the solution is not a whole number, you will need to round up to the nearest whole number since you can't have a fractional number of passengers.