Write and solve an equation to find out the prices at which the theater would earn $1,500 in profit from the comedy show each weekend. Show your reasoning.
Answers
SOLUTION
COMPLETE QUESTION
A community theater uses the function p(d) = 4d² + 200d - 100 to model the profit (in dollars) expected in a weekend when the tickets to a comedy show are priced at d dollars each. Write and solve an equation to find out the prices at which the theater would earn $1,500 in profit from the comedy show each weekend
EVALUATION
Here it is given that the community theater uses the function p(d) = 4d² + 200d - 100 to model the profit (in dollars) expected in a weekend when the tickets to a comedy show are priced at d dollars each
Thus p(d) = 4d² + 200d - 100
Now we have to find the value of d when p(d) = 1500
p(d) = 1500
⇒ 4d² + 200d - 100 = 1500
⇒ 4d² + 200d - 1600 = 0
⇒ d² + 50d - 400 = 0
⇒ d² + 40d - 10d - 400 = 0
⇒ ( d + 40 ) ( d - 10 ) = 0
d + 40 = 0 gives d = - 40
d - 10 = 0 gives d = 10
FINAL ANSWER
Hence the required price = $ 10
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