Steven needs to buy t theme park tickets for himself and his family. Each ticket costs $80, and the number of tickets he needs to buy can be modeled by the expression t2 - 4t - 90 = 6 when t > 0. What is the total cost of the theme park tickets that Steven purchased?
A. $640
B. $800
C. $960
D. $1,120
Answer:C
Steven needs to buy t theme park tickets for himself and his family. Each ticket costs $80, and the number of tickets he needs to buy can be modeled by the expression t2 - 4t - 90 = 6 when t > 0. What is the total cost of the theme park tickets that Steven purchased?
A. $640 B. $800 C. $960 D. $1,120
Explanation: C Rearranging and factoring the expression provided in the question, we have t2 - 4t - 90 = 6 → t2 - 4t - 96 = 0 → (t - 12)(t + 8) = 0. Therefore, t - 12 = 0 and t + 8 = 0. t must then equal 12 or -8. If t represents the number of tickets Steven buys, then only t = 12 is consistent with the context of the question. If each ticket costs $80, Steven must have spent $80 · 12 = $960. This is (C).