Question

directions: complete the additional practice below before beginning the online practice game. be sure to check your answers with an adult and the key.

1. a volleyball team is renting buses and vans for a trip to a national competition. the buses can hold 40 people, and the vans can hold 10 people. including parent chaperones, players, and some family, there will be 100 people going on the trip.

a. write an equation that represents this scenario. be sure to identify the meaning of the variables.
b. if 6 vans are rented, how many buses will need to be rented?
c. if 2 buses are rented, how many vans will need to be rented?
d. if 2 buses are rented, how many people will ride in vans?
e. if the team members prefer to ride in vans and do not want to rent any buses, how many vans will they need to rent?

Explanation:

Step1: Define variables and write equation

Let \( B = \) number of buses, \( V = \) number of vans. Total people: \( 40B + 10V = 100 \)

Step2: Substitute \( V=6 \) into equation

\( 40B + 10(6) = 100 \) → \( 40B + 60 = 100 \) → \( 40B = 40 \) → \( B=1 \)

Step3: Substitute \( B=2 \) into equation

\( 40(2) + 10V = 100 \) → \( 80 + 10V =100 \) → \( 10V=20 \) → \( V=2 \)

Step4: Calculate van riders with \( B=2 \)

Van capacity × vans: \( 10×2=20 \)

Step5: Substitute \( B=0 \) into equation

\( 0 +10V=100 \) → \( V=10 \)

Answer:

a. \( 40B + 10V = 100 \) (where \( B \) = number of buses, \( V \) = number of vans)
b. 1
c. 2
d. 20
e. 10