# Tickets sold to a school dance cost $4 and the projected attendance is 300. for every$0.10 increase in price the attendance will decrease by 5. what ticket price will generate $1237.5? ##### 1 Answer Aug 8, 2016 $4.50 or $5.50 #### Explanation: Attendance (A) given by: $A = 300 - 5 n$where $n$is every$0.10 over $4. Ticket price (T) given by: $T = 4 + 0.1 n$Total earnings (E) given by: $E = A \cdot T$$E = \left(300 - 5 n\right) \left(4 + 0.1 n\right)$$E = 1200 + 30 n - 20 n - 0.5 {n}^{2} = 1200 + 10 n - 0.5 {n}^{2}$We want $E = 1237.5$so $1237.5 = 1200 + 10 n - 0.5 {n}^{2}$Yielding a quadratic: $0.5 {n}^{2} - 10 n + 37.5 = 0$Multiply by 2 to get tidier numbers. This is not really necessary, just out of preference. ${n}^{2} - 20 n + 75 = 0$Could easily factorise by eye but will use quadratic formula for completeness. $n = \frac{20 \pm \sqrt{{\left(- 20\right)}^{2} - 4 \left(1\right) \left(75\right)}}{2}$$n = \frac{20 \pm \sqrt{400 - 300}}{2} = \frac{20 \pm 10}{2} = 15 \mathmr{and} 5$n = 5 implies T =$4.50

n = 15 implies T = \$5.50