Hello, I need assistance with my algebra homework very soon please

Question

Question 1.) A carpet cleaning business has 100 customers when they charge $125 for a cleaning. Research shows that every $5 reduction in price attracts another 20 customers. Which equation could be used to represent this situation, where x is the price per cleaning and R(x) is the total revenue?

A.) R(x) = −4x2 + 600x

B.) R(x) = −2x2 + 400x

C.) R(x) = 2x2 − 400x

D.) R(x) = 4x2 − 600x

Question 2.) The cost of renting a fishing boat is $25 per hour for the first 7 hours, $10 per hour for the next 10 hours, and $5 per hour for any additional hours. Identify the cost of renting the boat for 30 hours.

A.) $150

B.) $425

C.) $325

D.) $340

Please please just explain and solve please

Answer 1

Question 1: A is the correct answer.

If you list the price per cleaning vs. the # of customers, you get something like below

Price People

125 100

120 120

115 140

As price goes down, people go up. This would plot as a line with a negative slope which would be -4X where X is the price.

The # of people would be represented by Y = -4X + constant.

When Y = 100, X is 125, so the constant = 100 + 4 x 125 = 600, so Y = -4X + 600.

The revenue is X x Y = X(-4X + 600) = -4X² +600X which is answer A.

Answer 2

Question 1.)

R(x) = (125 - 5x)(100 + 20x)

Question 2.)

7($25) + 10($10) + 13($5) = ?