Question

A carpet cleaning business has 100 customers when they charge $125 for a cleaning. Research shows that every $10 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?

R(x) = −2x2 − 350x
R(x) = 2x2 − 350x
R(x) = 2x2 + 350x
R(x) = −2x2 + 350x

Answer 1

Answer: The equation that could be used to represent this situation is:

R(x) = (100 + 20n)(125 - 10n)

where x is the price per cleaning, n is the number of times the price is reduced by $10, and R(x) is the total revenue.

Initially, the price is $125 and there are 100 customers, so the revenue is:

R(125) = 100(125) = 12500

If the price is reduced by $10, the new price is $115, and the number of customers increases by 20:

R(115) = (100 + 20)(115) = 13800

Continuing in this way, the revenue for each price reduction can be calculated. The total revenue is the sum of all the revenues:

R(x) = (100 + 20n)(125 - 10n)

R(x) = 12500 + 2000n - 1000n^2

Simplifying this equation, we get:

R(x) = -1000n^2 + 1000n + 12500

Therefore, the correct equation to represent this situation is:

R(x) = -2x^2 + 350x.

Explanation: