The booster club at Preston Hills High School is selling tickets to a fundraiser for the marching band. The club wants to figure out how much to charge per ticket to make $3,600, which is the total cost for six new trumpets. Based on previous fundraisers, the expression –4p+260 can be used to estimate the number of tickets the booster club will sell given the ticket price, p.Which equation can the booster club use to estimate a ticket price that will raise $3,600 in revenue?3,600p=p(–4p+260)3,600=p(–4p+260)What is the lowest ticket price the booster club can use to make $3,600 in revenue?
Question
The booster club at Preston Hills High School is selling tickets to a fundraiser for the marching band. The club wants to figure out how much to charge per ticket to make 3,600 in revenue?3,600p=p(–4p+260)3,600=p(–4p+260)What is the lowest ticket price the booster club can use to make $3,600 in revenue?
Solution
The equation that the booster club can use to estimate a ticket price that will raise $3,600 in revenue is 3,600 = p(–4p+260).
To find the lowest ticket price, we need to solve this equation for p.
Step 1: Distribute the p on the right side of the equation: 3,600 = -4p^2 + 260p
Step 2: Rearrange the equation to set it equal to zero: 0 = -4p^2 + 260p - 3,600
Step 3: Divide the entire equation by -4 to simplify: 0 = p^2 - 65p + 900
Step 4: Factor the quadratic equation: 0 = (p - 15)(p - 60)
Setting each factor equal to zero gives the solutions p = 15 and p = 60.
Therefore, the lowest ticket price the booster club can use to make 15.
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