Final answer:
To determine the number of gym members in equilibrium, we set up a system of equations based on the given percentages of members likely to attend or not attend the gym. Solving the equation G = 0.60G + 0.40(200 - G) shows that 200 members will be at the gym in equilibrium.
Step-by-step explanation:
To find out how many members will be at the gym in equilibrium, we need to set up a system of equations. Let's denote the number of members who go to the gym on a certain day as G, and the number of members who do not go to the gym that day as N. Based on the information provided, we have a total of 200 members, and in equilibrium, the number of people who attend and who don't attend the gym will not change from day to day.
The system of equations based on the given percentages will be:
- 60% of G will go again the next day.
- 40% of N (which is 200 - G because N + G = 200) will go the next day.
In equilibrium, the number of members going to the gym (G) plus the number of members who will go the next day from those who didn't go (40% of N) will equal the current number of members at the gym (G). We can write the equation as follows:
G = 0.60G + 0.40(200 - G)
Solving this equation gives:
0.60G + 0.40 × 200 - 0.40G = G
0.20G = 0.40 × 200
G = (0.40 × 200) / 0.20
G = 400 / 0.20
G = 200 members
Therefore, the number of members that will be at the gym in equilibrium is 200.