Section: Mathematics Usage

35) 100 people will attend a dance if tickets cost $30 each. For each $5 increase in price, 10 fewer people will attend. What price will deliver the maximum dollar sales?

1. 30
2. 35
3. 40
4. 45
5. 50

The formula to solve this equation is M = (cost of ticket)(number of tickets). Thus

M = (30 + 5x)(100 - 10x).

The roots of this symmetric curve are 10 and -6 and the line of symmetry is x = 2. Plug 2 in for x in the original equation, and the result is 40.