Maths · Quadratic equations in real and complex number systems and their solutions
A family is going to a theme park having members in the family. Each ticket cost
A family is going to a theme park having \( t \) members in the family. Each ticket costs \( \$ 80, \) and the number of tickets needs to be bought can be calculated from the expression \( t^{2}- \) \( 4 t-90=6 \) when \( t>0 . \) What is the total cost of the theme park tickets that the family paid?
- A. \( \$ 640 \)
- B. \( \$ 800 \)
- C. \( \$ 960 \)
- D. \( \$ 1,120 \)
Step-by-step solution
Solve the equation t^2 - 4t - 90 = 6 to get t^2 - 4t - 96 = 0. Factor to (t-12)(t+8)=0, so t=12 (since t>0). Total cost = 12 tickets × $80 = $960.
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