Question

Over the summer, Bryce offers landscaping services throughout his community. His most popular request is to install small flower beds in his neighbors' yards. After conducting a survey of his neighbors, Bryce determines that if he charges x dollars per flower bed, he will install
–
3x+270 flower beds this summer.
The materials to make each flower bed cost Bryce $10. So, he will earn x–10 dollars in profit for each flower bed he installs.
Which equation can Bryce use to predict the price he can charge per flower bed to earn $4,500 in profit this summer?
What two prices can Bryce charge per flower bed to earn exactly $4,500 in profit this summer?

Answer 1

Let x be the price per flower bed. Total profit = (number of beds) × (profit per bed) = (−3x + 270)(x − 10). Set this equal to 4500:

(−3x + 270)(x − 10) = 4500.

Solve:
-3x^2 + 300x − 2700 = 4500
=> 3x^2 − 300x + 7200 = 0
=> x^2 − 100x + 2400 = 0
=> (x − 60)(x − 40) = 0.

So x = $60 or x = $40. These two prices each yield $4,500 total profit.