At the beginning of the year,40% of the pupils 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 numbers of art club members at the beginning of the year.

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.

Well, well, well! It seems we have a puzzle to solve here. Let's break it down and have some fun with numbers.

At the beginning of the year, 40% of the art club members were boys. But hold your laughter, because we don't know the total number of members at that point. Let's call it x.

So, the number of boys in the art club at the beginning of the year would be 40% of x, which is 0.4x.

In the middle of the year, 25% of the girls left. Poor girls, maybe they decided to join a knitting club instead. Anyway, we now have 75% of the girls left. But remember, we still don't know the total number of girls, so let's call that y.

We also had 8 more boys join the club. So now we have (0.4x + 8) boys in total.

The total number of members in the art club is given as 42. That means the sum of boys and girls is 42. Are you still following me? I hope my clown math isn't too confusing!

So, we have the equation: 0.4x + 8 + y = 42.

Now, let's use this equation to find the value of x, the total number of art club members at the beginning of the year. Keep smiling and get ready for some calculations!

0.4x + 8 + y = 42.

Now, if you have a sense of humor, you can solve this equation for x. Trust me, it won't be as scary as a creepy clown!

*x = 42 - 8 - y*

And that's it! We found x, the total number of art club members at the beginning of the year. I hope I brought a smile to your face while solving this little puzzle of ours.

Let's break down the information given step-by-step:

Step 1: At the beginning of the year, 40% of the pupils in the art club were boys.
Let the total number of members at the beginning of the year be B.
So, the number of boys at the beginning of the year = 40% of B = 0.4B.

Step 2: In the middle of the year, 25% of the girls left.
Let the number of girls at the beginning of the year be G.
So, the number of girls who left = 25% of G = 0.25G.

Step 3: 8 more boys joined the art club.
Therefore, the total number of boys after 8 more joined = 0.4B + 8.

Step 4: The number of members became 42.
The total number of members at the beginning of the year = Number of boys after 8 more joined + Number of girls who left + Number of girls who remained.
Therefore, B = (0.4B + 8) + (0.25G) + (G - 0.25G).
Simplifying the equation, we get: B = 0.65B + 8.75G.

Step 5: We need to find the total number of art club members at the beginning of the year.
From Step 4, we have the equation: B = 0.65B + 8.75G.
But we don't have enough information to solve for B or G with just one equation.

To find a unique solution, we need either the value of B or G. Without that information, we can't determine the total number of art club members at the beginning of the year.

To find the total number of art club members at the beginning of the year, we need to break down the problem into steps:

Step 1: Calculate the number of boys in the art club at the beginning of the year.
Let's assume the total number of pupils in the art club at the beginning of the year is "x". Since 40% of the pupils were boys, we can calculate the number of boys using the equation: 40% * x = 0.4x.

Step 2: Calculate the number of girls in the art club at the beginning of the year.
Since the total number of art club members is equal to the sum of the number of boys and girls, we can calculate the number of girls using the equation: Total members - Number of boys = Number of girls.

Step 3: Calculate the number of girls in the art club after some members left.
Since 25% of the girls left, we can calculate the remaining number of girls using the equation: Number of girls at the beginning of the year - (25% * Number of girls at the beginning of the year) = Number of girls after some left.

Step 4: Calculate the total number of art club members after boys joined and girls left.
The total number of members is equal to the sum of the number of boys at the beginning of the year, the number of boys who joined, the number of girls after some left, and the number of boys who left.

Step 5: Solve for the total number of art club members at the beginning of the year.
Since the problem states that the total number of members became 42 after some changes, we can set up the equation: Total members = Number of boys at the beginning of the year + Number of boys who joined + Number of girls after some left + Number of boys who left.

By substituting the values obtained in each step into the equation, we can solve for the total number of art club members at the beginning of the year.