At the beginning of the year, 40% of the students in the Art Club were boys. In the middle of the year, 25% of the girls left but 8 more boys joined the Art Club. The number of members became 42. Find the total number of Art Club members at the beginning of the year.
42=.4AC+8 +.6AC(1-.25)
find AC, the total number of art club at start of year.
42-8=AC(.4+.75*.6)
34=AC(.85) >>>>>AC=40 check that.
Thanks!
Let's assume the total number of students in the Art Club at the beginning of the year is "x".
According to the given information:
- 40% of x were boys, so the number of boys at the beginning of the year is 0.4x.
- The remaining students were girls, so the number of girls at the beginning of the year is (1-0.4) x = 0.6x.
In the middle of the year:
- 25% of the girls left, so the number of girls that left is 0.25 * 0.6x = 0.15x.
- The number of girls that remained is now 0.6x - 0.15x = 0.45x.
- 8 more boys joined, so the number of boys is now 0.4x + 8.
The total number of members at this point is given as 42, so we can set up the equation:
0.45x + 0.4x + 8 = 42
Combining like terms:
0.85x + 8 = 42
Subtracting 8 from both sides:
0.85x = 42 - 8
0.85x = 34
Dividing both sides by 0.85:
x = 34 / 0.85
x = 40
Therefore, the total number of Art Club members at the beginning of the year is 40.
To solve this problem, we need to find the total number of Art Club members at the beginning of the year. Let's break down the information given.
At the beginning of the year, 40% of the students in the Art Club were boys. This means that 60% of the students were girls.
Let's assume the total number of students in the Art Club at the beginning of the year is x.
The number of boys in the Art Club at the beginning of the year would be 40% of x, which is 0.4x.
The number of girls in the Art Club at the beginning of the year would be 60% of x, which is 0.6x.
In the middle of the year, 25% of the girls left. This means that 75% (100% - 25%) of the girls remained.
The number of girls left in the Art Club after some members left would be 75% of 0.6x, which is 0.75 * 0.6x = 0.45x.
The number of boys in the Art Club after 8 more boys joined would be 0.4x + 8.
The total number of Art Club members became 42, so we can set up an equation:
0.45x + (0.4x + 8) = 42
Now, we can solve this equation to find the value of x, which represents the total number of Art Club members at the beginning of the year.