Chapter 2.1, Problem 32E

a.

To determine

To find: the correct system of equations from the given options that could be used by newspaper reader to determine the number of tickets for each team.

Answer to Problem 32E

B

Explanation of Solution

Given information:

The given statements are as follows:

1. Total number of seats = 30000
2. Spartans are four times than the visiting team’s fans
3. Number of tickets for Spartans and visiting team’s fans is represented by $S$ and $V$ respectively.

The given options are as follows:

A. $\begin{array}{l}4S+4V=30000\\ S=4V\end{array}$

B. $\begin{array}{l}S-4V=0\\ S+V=30000\end{array}$

C. $\begin{array}{l}S+V=30000\\ V-4S=0\end{array}$

Calculation:

Since, the total number of seats (i.e. 30000) is occupied by two teams S and V. Thus, the equation becomes,

  $S+V=30000$

Since, Spartans are four times than the visiting team’s fans. The equation can be written as follows:

  $\begin{array}{l}S=4V\\ S-4V=0\text{ [Rearranged]}\end{array}$

The correct set of equation is as follows:

  $\begin{array}{l}S-4V=0\\ S+V=30000\end{array}$

Therefore, the correct option is B.

b.

To determine

To find: the number of tickets for each team.

Answer to Problem 32E

  $\begin{array}{l}S=24000\\ V=6000\end{array}$

Explanation of Solution

Given information:

Total number of seats = 30000

Spartans are four times than the visiting team’s fans.

Number of tickets for Spartans and visiting team’s fans is represented by $S$ and $V$ respectively.

The correct system of equation is as follows:

  $\begin{array}{l}S=4V\mathrm{...}\left(1\right)\\ S+V=30000\mathrm{...}\left(2\right)\end{array}$

Calculation:

Substitute the value of S in equation (2) and evaluate V as follows:

  $\begin{array}{c}S+V=30000\\ 4V+V=30000\\ 5V=30000\\ V=\frac{30000}{5}\\ =6000\end{array}$

Now, substitute the value of V in equation (1) and evaluate S as shown below.

  $\begin{array}{c}S=4V\\ =4\left(6000\right)\\ =24000\end{array}$

Therefore, the number of tickets for S and V is 24000 and 6000 respectively.