Question

At a math competition, each team wrote 2 questions for each of the other teams. All of the teams then solved the questions that were written for them and the judges scored all of the questions. The judges scored a total of 40 questions.

Let n be the number of teams at the competition.
Define each of the unknowns in terms of n by matching it with its meaning or description. please help!!!!

Answer 1

The total number of questions asked at the math competition can be expressed as 2n(n - 1), where n is the number of teams. Since the judges scored a total of 40 questions, you can write the equation 2n(n - 1) = 40 to solve for n.

Step-by-step explanation:

The question is asking for a way to define the unknown variables in terms of the number of teams n at a math competition. Assuming that each of the n teams writes 2 questions for each of the other teams, which leads to a total score of 40 questions by the judges.

Since each team writes 2 questions for all other teams, we can express the total number of questions asked as 2n(n - 1), because there are n teams and each one writes questions for n - 1 other teams (not including itself). However, we know that the judges scored a total of 40 questions, which allows us to write the following equation:

2n(n - 1) = 40

To find the number of teams n, you must solve the quadratic equation. The solution of this equation will give you the number of teams that participated in the competition.