Sightseeing boat and writing equation

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In summary: This is represented by the equation p=10-.05(x-150). So, for example, if there are 160 passengers, we would have:p=10-.05(160-150)p=10-.05(10)p=10-.50p=9.50This means that for 160 passengers, the price per passenger would be \$9.50 instead of the base price of \$10. This formula allows for the boat company to reduce the rate for all passengers when there are more than the minimum of 150 passengers.Now, to find the maximum income for the boat company, we need to use the second equation given, which is y=x(17.5-0.05x). This
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mathgeek7365
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A sightseeing boat is chartered by a social club at the rate of $10 per person. The club guarantees the boat company a minimum of 150 people. The boat company agrees to reduce the rate for all passengers by 5 cents a person for each additional person over the 150 minimum. Write and solve an equation to find the number of passengers that will yield the boat company the maximum income.

Let y= total income
x= # of passengers
p= price per passenger

Our problem is the logic behind the equations/how to get the equations. Her teacher said that:

-As long as there are at least 150 passengers, p=10-.05(x-150). Which can be simplified to p=17.5-0.05n.
•She does not understand the x-150 part. Or why you multiply it by 10-0.05.

-The total revenue collected is x times the price per passenger (p), so y=x(17.5-0.05x), which in it's expanded form is y= -0.05x22+17.5x.
•She completely understand everything here.

She can pretty much solve the equation, she just needs to know why these equations work. Thanks for anything you can assist her with.
 
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  • #2
mathgeek7365 said:
...-As long as there are at least 150 passengers, p=10-.05(x-150). Which can be simplified to p=17.5-0.05n.
•She does not understand the x-150 part. Or why you multiply it by 10-0.05...

First, we are not multiplying $(x-150)$ by $10-0.05$...that would look like:

\(\displaystyle p=(10-.05)(x-150)\)

What we are doing is taking the base price of \$10 per passenger, and for each passenger in excess of 150, or $x-150$, we are subtracting 5 cents.
 

FAQ: Sightseeing boat and writing equation

What is a sightseeing boat?

A sightseeing boat is a watercraft designed for leisurely tours of scenic locations, such as rivers, lakes, or coastlines. These boats often have open decks and large windows to provide passengers with a clear view of the surrounding scenery.

What is the purpose of writing an equation for a sightseeing boat?

Writing an equation for a sightseeing boat can help determine its speed, fuel efficiency, and other important factors for its operation. It can also aid in the design and construction process of the boat.

What factors are typically included in an equation for a sightseeing boat?

An equation for a sightseeing boat may include variables such as the boat's weight, engine power, water resistance, and wind conditions. It may also take into account the boat's dimensions, such as length and width.

How does a sightseeing boat's equation differ from other types of boats?

The equation for a sightseeing boat may differ from other types of boats due to its focus on leisure and tourism rather than transportation or commercial use. This may result in different variables being included in the equation.

Why is it important to understand the equation for a sightseeing boat?

Understanding the equation for a sightseeing boat can help ensure the safety and efficiency of the boat's operation. It can also aid in making informed decisions about the design, maintenance, and performance of the boat.

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