Question

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 $t^2-4t-90=6$ when $t>0$. What is the total cost of the theme park tickets that the family paid?

• A. $\$640$
• B. $\$800$
• C. $\$960$
• D. $\$1,120$

Answer 1

Answer: (C)

$\$960$

Let the number of family members that are going to the theme park is $t$.

The number of tickets needs to be bought is calculated from the expression,

$\Rightarrow t^2-4t-90=6$

$\Rightarrow t^2-4t-90-6=0$

$\Rightarrow t^2-4t-96=0$

$\Rightarrow t^2-12t+8t-96=0$

$\Rightarrow t(t-12)+8(t-12)=0$

$\Rightarrow (t-12)(t+8)=0$

$\therefore t=12or-8$

Then number of family member is not be negative, so $t=12$

Cost of one ticket $=$80$

$\therefore$ cost of $12$ ticket=$80\times 12=$960$