Question

Spartan Stadium at San Jose State University in California has a seating capacity of about 30,000. A newspaper article states that the Spartans get four times as many tickets as the visiting team. Suppose S represents the number of tickets for the Spartans and V represents the number of tickets for the visiting team’s fans. Which system could be used by a newspaper reader to determine how many tickets each team gets? a. 4S + 4V = 30,000 S = 4V c. S + V = 30,000 V - 4S = 0 b. S - 4V = 0 S + V = 30,000

Answer 1

The answer is the option b: b.
`\left \{ {{S-4V=0} \atop {S+V=30,000}} \right. \\`

The explanation is shown below:

1. You have that S represents the number of tickets for the Spartans and V represents the number of tickets for the visiting team's fans, and the seating capacity of the Spartan Stadium is 30,000. Therefore, the total number of tickets is 30,0000:

`S+V=30,000`

2. If the Spartans get four times as many tickets as the visiting team, you have:

`S=4V`

`S-4V=0`

3. If you solve the system of equations by the method of substitution, you obtain:

`S+V=30,000`

`4V+V=30,000`

`V=6,000`

4. Calculate S:

`S+6,000=30,000`

`S=24,000`