Question

Fifty-six (56) students from the robotics team went to a competition match at the Jacob Javits Center. Some students rode in vans that hold 8 people each, and some students rode in cars that hold 4 people each. If there were a total of 12 vehicles, find out how many of each type of vehicle was used.

A. 4 vans and 8 cars
B. 6 vans and 6 cars
C. 8 vans and 4 cars
D. 10 vans and 2 cars

Answer 1

By setting up a system of equations, we find that 2 vans and 10 cars were used to transport the students. However, this answer is not listed in the given options, indicating a potential discrepancy that needs to be addressed or the question may need to be revisited.

Step-by-step explanation:

To determine how many vans and cars were used by the 56 students from the robotics team, we can set up a system of equations based on the information given. Let v be the number of vans and c be the number of cars. Each van holds 8 people, and each car holds 4 people. We also know there were a total of 12 vehicles.

The two equations are as follows:

• 8v + 4c = 56 (total number of students)
• v + c = 12 (total number of vehicles)

To solve the system, we can multiply the second equation by 4 to eliminate the variable c:

• 8v + 4c = 56
• 4v + 4c = 48

Now subtract the second modified equation from the first original equation:

• (8v + 4c) - (4v + 4c) = 56 - 48
• 4v = 8

Divide by 4 to find the number of vans:

• v = 2

Substitute v into the second original equation to find the number of cars:

• 2 + c = 12
• c = 10

Therefore, there were 2 vans and 10 cars used. However, since this answer is not listed in the provided options, we may double-check our calculations or the question. If double-checking confirms they are correct, we would communicate to the student that none of the given options A, B, C, or D correctly fulfill the equations based on the information provided.