Please help me as soon as possible please with algebra homework

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

A) R = Price × Quantity

Price = x = 125-5n --> n = (125-x)/5

Quantity = 100+20n = 100 + 20(125-x)/5 = 100 + 500 -4x = 600-4x

R = x(600-4x) = -4x²+600x <--- Answer A

B) For 30 hours

Cost = 7(25) + 10(10) + 5(30-17) = 175 + 100 + 5(13) = $340 <--- Answer D

Answer 2

Hello, Jonathon,

Question 1 was a little difficult, until I made the assumption that the "2" following the fitrst x is actual ^2. So the first equation is actually R(x) = −4x^2 + 600x, and the same for the others.

Make a table of cost/cleaning and number of customers. I added data points as per the wording as to how many more customrs are gained for each $5 drop in price. Add a coulmn for total sales by multiplying the rate times the customers.

I increased the customers by 20 for each $5 step reduction in price. We see that the revenue increases as the price drops. Then I siomply used these points in the equations to see which equation would correctly predict the total revenue when the cost/job is $115.

The first option, y = -4x^2 + 600x works:

1. I added the cost for the first 7 hours (25*7 = $175), to that of the next 10 hours (10*10 = $100), and then added the remaining 13 hours (13*5 = $65) for a total of $340 for the 30 hours.

Bob