Consider the equation x over 5 minus 2 = 11, where x represents the number of basketball players that have signed up for a new league. What is a possible scenario that would be modeled by this equation? Consider how many teams in the league and the number of players on each team this equation could describe
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To understand the possible scenario that would be modeled by the equation x/5 - 2 = 11, we need to solve the equation and interpret the solution in the context of the problem.
Let's solve the equation step by step:
1. Start with the given equation: x/5 - 2 = 11
2. Add 2 to both sides of the equation to isolate the term containing x: x/5 = 13
3. Multiply both sides of the equation by 5 to eliminate the fraction: 5(x/5) = 5(13)
Simplifying: x = 65
Therefore, the solution to the equation is x = 65. This means that the number of basketball players that have signed up for the league is 65.
Now, let's consider how this equation could describe a possible scenario:
Let's assume that the scenario is a new basketball league, and the equation is used to determine the number of players. In this case, we can interpret the equation to mean the following:
- The variable x represents the total number of basketball players in the league.
- The equation x/5 - 2 = 11 indicates that each team in the league has 5 players, and 2 players have already been assigned to a team.
- The right side of the equation, 11, represents the remaining number of players that need to be assigned to teams.
- By solving the equation, we found that there must be a total of 65 players in the league (x = 65).
- Based on this scenario, we can conclude that there are 13 teams in the league, each with 5 players, and 2 players have already been assigned to teams. The remaining 11 players still need to be assigned to teams.
Therefore, a possible scenario that could be modeled by the equation x/5 - 2 = 11 is a new basketball league with 13 teams and 65 players, where each team has 5 players.