Consider the equation StartFraction x over 5 EndFraction 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
geez - ever hear of using actual numbers?
Instead of
StartFraction x over 5 EndFraction minus 2 = 11
just type
x/5 - 2 = 11
Since there are 5 players on a team, if there are x players, then there are x/5 teams. See what you can do with that.
Well, if we take a humorous approach, one possible scenario that could be modeled by this equation is a league with one team that has a very specific number of players. Let's call them the "Super Slim Pickings" team.
In this scenario, since we have x players signed up for the new league, the equation becomes (x/5) - 2 = 11.
Now, let's solve for x and find out how many players the Super Slim Pickings team has. Adding 2 to both sides of the equation, we get (x/5) = 13. Multiplying both sides by 5, we find that x = 65.
So, in this wacky scenario, the "Super Slim Pickings" team has 65 players. Quite a large team for a one-team league! Looks like they'll have to take turns to get any actual playing time, or maybe they'll just turn into their own cheerleading squad. Who needs opponents when you have 65 teammates, right?
The equation describes a scenario where there are multiple teams in a basketball league and the equation is used to determine the number of players on each team. Let's break it down step by step:
Step 1: Start with the equation:
StartFraction x over 5 EndFraction minus 2 = 11
Step 2: To solve this equation, we will isolate x by performing inverse operations. We can start by adding 2 to both sides of the equation:
StartFraction x over 5 EndFraction minus 2 + 2 = 11 + 2
StartFraction x over 5 EndFraction = 13
Step 3: To get rid of the fraction, we can multiply both sides of the equation by 5:
5 * StartFraction x over 5 EndFraction = 13 * 5
x = 65
Step 4: The value of x represents the number of basketball players that have signed up for the league. In this scenario, the equation suggests that there are 65 players in total.
Step 5: We can interpret this in terms of teams in the league. Since we don't have information about the number of teams or the distribution of players among the teams, we cannot determine the exact number of players on each team. However, we can consider some possible scenarios:
- If there are 2 teams in the league, each team could have 32 players with one team having 33 players.
- If there are 5 teams in the league, each team could have 13 players with one or more teams having 14 players.
These are just a few examples, and there are many other possible scenarios that could fit the equation. The actual distribution of players among the teams would depend on the specific details of the league.
To find a possible scenario that would be modeled by this equation, we need to solve it and interpret the solution in the context of a basketball league.
The given equation is StartFraction x over 5 EndFraction minus 2 = 11.
To solve for x, we can isolate x by undoing the operations in reverse order.
First, add 2 to both sides of the equation:
StartFraction x over 5 EndFraction minus 2 + 2 = 11 + 2
StartFraction x over 5 EndFraction = 13
Next, multiply both sides of the equation by 5 to get rid of the fraction:
5 * StartFraction x over 5 EndFraction = 13 * 5
x = 65
So, the solution to the equation is x = 65.
In the context of a basketball league, the solution x = 65 would mean that there are 65 basketball players who have signed up for the new league. This scenario could describe a league with multiple teams, where each team has a different number of players.
For example, if there are 5 teams in the league, one possible distribution of players could be:
- Team 1: 12 players
- Team 2: 15 players
- Team 3: 8 players
- Team 4: 20 players
- Team 5: 10 players
In this scenario, the total number of players in the league is 12 + 15 + 8 + 20 + 10 = 65, which matches the solution to the equation.