Chapter 1, Problem 4SAP

To determine

To select: minimum number of adult tickets sold from the given options.

Answer to Problem 4SAP

E. 11

Explanation of Solution

Given information:

Cost of student ticket =$2

Cost of adult ticket =$5

Total tickets sold = 30

Total sale must exceed = $90

The given options are as follows:

1. 7
2. 8
3. 9
4. 10
5. 11

Calculation:

Let the number of tickets for students and adult be x and y respectively.

According to the question, the equation will be as follows:

  $\begin{array}{l}x+y=30\mathrm{...}\left(1\right)\\ 2x+5y>90\mathrm{...}\left(2\right)\end{array}$

Rearrange the first equation and find the value of x as shown below.

  $\begin{array}{c}x+y=30\\ x=30-y\end{array}$

Substitute the value of x in equation (2) and solve the equation as shown below.

  $\begin{array}{c}2x+5y>90\\ 2\left(30-y\right)+5y>90\\ 60-2y+5y>90\\ 60+3y>90\\ 3y>90-60\\ 3y>30\\ y>\frac{30}{3}\\ y>10\end{array}$

So, in order to exceed the sale by $90, the minimum number of adult tickets that should be sold is 11. Thus, option E is correct.