Question

1. pit tickets cost $49 and general admission tickets cost $20. if 350 tickets were sold, and revenue earned for the tickets was $9175. how many of each ticket were sold?

1. sometimes you walk to campus and other times you take your bike. it takes you 20 minutes to walk and only 6 minutes to bike to campus. if your average speed is 7 miles per hour faster when you bike to campus, what is your average speed for walking and for biking?

Explanation:

Problem 3

Step1: Define variables

Let \( x \) be the number of pit tickets, \( y \) be the number of general admission tickets.
We have two equations:

1. \( x + y = 350 \) (total tickets)
2. \( 49x + 20y = 9175 \) (total revenue)

Step2: Solve the system

From the first equation, \( y = 350 - x \). Substitute into the second equation:
\( 49x + 20(350 - x) = 9175 \)
\( 49x + 7000 - 20x = 9175 \)
\( 29x = 9175 - 7000 \)
\( 29x = 2175 \)
\( x = \frac{2175}{29} = 75 \)

Step3: Find \( y \)

\( y = 350 - 75 = 275 \)

Step1: Convert time to hours

Walking time: \( 20 \) minutes \( = \frac{20}{60} = \frac{1}{3} \) hours.
Biking time: \( 6 \) minutes \( = \frac{6}{60} = \frac{1}{10} \) hours.

Let \( w \) be walking speed (mph), \( b \) be biking speed (mph). We know \( b = w + 7 \), and distance \( d = w \times \frac{1}{3} = b \times \frac{1}{10} \).

Step2: Substitute \( b \)

\( \frac{w}{3} = \frac{w + 7}{10} \)
Multiply both sides by 30: \( 10w = 3(w + 7) \)
\( 10w = 3w + 21 \)
\( 7w = 21 \)
\( w = 3 \)

Step3: Find \( b \)

\( b = 3 + 7 = 10 \)

Answer:

Pit tickets: 75, General admission tickets: 275

Problem 4