Question

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.

Answer 1

Let's start by assuming that the total number of students in the Art Club at the beginning of the year was x.

We know that 40% of the students were boys, which means that 60% were girls.

So, the number of boys in the Art Club at the beginning of the year was 0.4x, and the number of girls was 0.6x.

In the middle of the year, 25% of the girls left, which means that 0.25(0.6x) = 0.15x girls left.

At the same time, 8 more boys joined the Art Club, so the total number of boys became 0.4x + 8, and the total number of girls became 0.6x - 0.15x = 0.45x.

We also know that the total number of members became 42, so we can write an equation:

0.4x + 8 + 0.45x = 42

Simplifying and solving for x, we get:

0.85x + 8 = 42

0.85x = 34

x = 40

Therefore, the total number of Art Club members at the beginning of the year was x = 40.

Answer 2

At beginning of year:

X members in art club.

0.4X boys.

0.6X girls.

In middle of year:

0.75 * 0.6X = 0.45X girls remaining.

0.4X+8 boys remains.

0.45x + 0.4x+8 = 42.

X = 40 At beginning of year.