The n soccer players on a team traveled to a game in 2 vans. Each van had seating for p players. One van was full and the other had 2 empty seats. Which of the following represents n in terms of p?

Rationale

n = 2p - 2.

To find the total number of players, we note that one van is full with p players, and the other van has 2 empty seats, meaning it carries (p - 2) players. Therefore, the total number of players n is the sum of players in both vans: n = p + (p - 2), simplifying to n = 2p - 2.

A (n = 2p + 2) YOUR ANSWER

This equation suggests that the total number of players is 2 more than twice the seating capacity of both vans. However, this does not account for the 2 empty seats in the second van, leading to an overestimation of the actual number of players.

B (n = 2p - 2) CORRECT

This correctly represents the total number of players on the team. It combines the full van's capacity (p) with the number of players in the second van, which is reduced by the 2 empty seats, leading to the correct expression of n.

C (n = 2(p - 2)) YOUR ANSWER

This choice implies that the total number of players is double the number of players in the second van, which is incorrect. It does not reflect the total capacity of both vans, as it disregards the full van's contribution.

D (n = p + 2) YOUR ANSWER

This representation suggests that the total number of players is simply the full capacity of one van plus 2, not accounting for the players in the second van. This fails to include the true contribution of both vans and thus misrepresents the total.

Conclusion

The equation n = 2p - 2 accurately encapsulates the scenario by accounting for the full capacity of one van and the players in the second van, adjusted for the two empty seats. This illustrates the importance of careful consideration of each van's capacity when determining the total number of players on the team.

The n soccer players on a team traveled to a game in 2 vans. Each van had seating for p players. One van was full and the other had 2 empty seats. Which of the following represents n in terms of p?

n = 2p - 2.

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