bobs band, laser trio, booked a venue to perform next weekend. they want to know how much to charge per…
bobs band, laser trio, booked a venue to perform next weekend. they want to know how much to charge per ticket to make $700 in revenue, since thats how much they just spent on a new drum set. based on past performances, the expression -5p + 135 can be used to predict the number of tickets the band will sell based on the ticket price, p. which equation can the band use to estimate the ticket price that will make them $700 in revenue? 700 = p(-5p + 135) 700p = p(-5p + 135) what two ticket prices will make the band exactly $700 in revenue? $ or $
Answer
Explanation:
Step1: Recall revenue formula
Revenue = Price × Quantity. The price of a ticket is $p$, and the quantity of tickets sold is given by the expression $- 5p + 135$, and the desired revenue is $700$. So the equation is $700=p(-5p + 135)$.
Step2: Rearrange the equation
Expand $700=p(-5p + 135)$ to get $700=-5p^{2}+135p$, or $5p^{2}-135p + 700 = 0$. Divide through by 5: $p^{2}-27p + 140=0$.
Step3: Factor the quadratic equation
We need to find two numbers that multiply to 140 and add up to 27. The numbers are 20 and 7. So $p^{2}-27p + 140=(p - 20)(p - 7)=0$.
Step4: Solve for $p$
If $(p - 20)(p - 7)=0$, then $p-20 = 0$ or $p - 7=0$. So $p = 20$ or $p=7$.
Answer:
First part: $700 = p(-5p + 135)$ Second part: $7$ or $20$