Amarina rents party boats for large social gatherings. they charge the following amounts for a 2 hour rental. 10 people for $165, 20 people for $192.50, 35 people for $233.75, and 50 people for $275. a) write an equation that represents the data. b) what are the intercepts if the graph of your equation? what is the slope? what do they mean in this context? c)use your equation to predict the cost of providing a party boat for 75 people. d) the marina actually charges $460 for 75 people . what might be a reason for the difference?

An equation that represents the data would be y=2.75x+137.50. The y-intercept of the graph is 137.50, which represents the base cost of a boat rental.  The slope of the graph is 2.75, which represents the rate, or cost per person.  If we use this equation to solve for the cost of boat rental for 75 people, we would get a total of $343.75.  A reason the marina might charge more for 75 people could be the need for a second boat and/or additional workers to handle the additional guests.  

Step-by-step explanation:

The problem gives you four sets of ordered pairs: (10, 165); (20, 192.50); (35, 233.75) and (50, 275).  Using these ordered pairs, you can either make a table, or use slope formula with two points to determine the rate of change.  For example, (192.50-165)/(20-10)= 2.75, which represents the slope or cost per person.  To find the y-intercept, or base cost to rent the boat, subtract the cost for 10 people ($27.50) from the $165 rental charge to get $137.50.  In order to find the cost for 75 people, you would plug in 75 for the variable 'x' and solve for 'y', which gives us $343.75.  Since the actual cost is different, we have to assume that there are additional fees associated with a certain number of people.  

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1