Final answer:
To find the total number of boys in the art club now, we first calculated the initial total number of students using a variable, figured out the number of girls who left, and then solved for the variable. There were initially 16 boys, and after 8 more boys joined, the total number of boys now is 24.
Step-by-step explanation:
To solve this problem, we need to find the number of boys in the art club before and after the changes that occurred during the year. Initially, we are told that 40% of the students were boys. Since we are not given the initial number of students, let's use a variable to represent that. Let the total number of students at the beginning be x. Therefore, the number of boys at the beginning would be 0.4x.
According to the question, 25% of the girls left the art club. Since boys made up 40% of the club, girls made up 60% (100% - 40%). We can calculate the number of girls who left as 25% of 60% of x, which is 0.25 × 0.6x = 0.15x. After these girls left, 8 more boys joined the club, increasing the number of boys to 0.4x + 8. At this point, the total number of club members became 42. We can now express the total number of students as the initial number of boys plus the additional boys minus the number of girls who left, plus the initial number of girls who did not leave, which gives us the equation:
0.4x + 8 + 0.6x - 0.15x = 42
Combining like terms gives 0.85x + 8 = 42. If we subtract 8 from both sides, we get 0.85x = 34. Then, dividing both sides by 0.85, we find x = 40. This means there were originally 40 students in the art club.
So, the total number of boys at the beginning was 40% of 40, which is 16 boys. After 8 more boys joined, the total number of boys in the art club now is 16 + 8 = 24.