2/5 of the children in an art club were girls. 1/4 of the girls and 5/6 of the boys took part in a competition. 12 boys did not take part in the competition.

a.) What percentage of the pupils in the art club did not take part in the competition?
b.) How many girls did not take part in the competition?

X = # of pupils in club.

2x/5 = # girls in club.
3/4(2x/5) = 6x/20 = 3x/10 = # of girls
not taking part.

B/6 = 12
B = 72 = # of boys in club.

2x/5 + 72 = X pupils.
2x + 360 = 5x
3x = 360
X = 120 pupils, total.

3x/10 = (3*120)/10 = 36 = Girls not
taking part.

a. (B+G)/X=((12+36)/120)*100%=40%.

b. 3x/10 = 360/10 = 36. Girls.

a.) What percentage of the pupils in the art club did not take part in the competition?

Let's solve this step by step.

First, we need to find out the total number of children in the art club. We know that 2/5 of the children were girls, so let's assume the total number of children in the art club is x. Therefore, the number of girls in the art club is (2/5)x.

Now, let's calculate the number of boys in the art club. Since the total number of children in the art club is x, and 2/5 of them are girls, the number of boys would be (3/5)x.

Now, let's determine the number of girls who took part in the competition. We are given that 1/4 of the girls took part in the competition, so the number of girls who participated would be (1/4) * (2/5)x = (1/10)x.

We are also given that 5/6 of the boys took part in the competition, so the number of boys who participated would be (5/6) * (3/5)x = (1/2)x.

Now, let's find out the total number of children who participated in the competition. We can add the number of participating girls and boys: (1/10)x + (1/2)x = (3/10)x + (5/10)x = (8/10)x = (4/5)x.

Since we know that 12 boys did not participate, we can determine the total number of boys in the art club: (3/5)x = 12. Dividing both sides by (3/5), we get x = 20.

Now, we can determine the number of children who did not take part in the competition. The total number of children in the art club is 20, and the number of children who participated in the competition is (4/5)x = (4/5) * 20 = 16. Therefore, the number of children who did not take part in the competition is 20 - 16 = 4.

To find the percentage, we divide the number of children who did not participate by the total number of children in the art club and multiply by 100.

Percentage of pupils who did not take part in the competition = (4/20) * 100 = 20%.

So, 20% of the pupils in the art club did not take part in the competition.

b.) How many girls did not take part in the competition?

We have already determined that the total number of girls in the art club is (2/5)x, and the number of girls who participated in the competition is (1/10)x. To find the number of girls who did not take part in the competition, we subtract the number of girls who participated from the total number of girls:

Number of girls who did not take part in the competition = (2/5)x - (1/10)x
= (4/10)x - (1/10)x
= (3/10)x.

Substituting the value of x as 20 (from the previous calculation), we can find the number of girls who did not take part in the competition:

Number of girls who did not take part in the competition = (3/10) * 20
= 6.

So, 6 girls did not take part in the competition.

To find the answers, let's break down the information step-by-step:

1. Start with the ratio of boys to girls in the art club: 2/5 girls and 3/5 boys.
2. Let's assume the total number of children in the art club is "x". Thus, the number of girls is (2/5) x and the number of boys is (3/5) x.
3. Out of the girls, 1/4 participated in the competition, so the number of girls who participated is (1/4)(2/5) x = (1/10) x.
4. Out of the boys, 5/6 participated in the competition, so the number of boys who participated is (5/6)(3/5) x = (1/2) x.
5. It is mentioned that 12 boys did not participate in the competition, so the number of boys who did participate is (3/5) x - 12.
6. We can now find the total number of children who participated in the competition by adding the number of girls and boys who participated: (1/10) x + (3/5) x - 12.
7. To find the percentage of students who did not take part, subtract the number who did participate from the total number of children in the art club (x): x - [(1/10) x + (3/5) x - 12].
8. Simplifying the equation gives us: x - (1/10)x - (3/5)x + 12.
9. Further simplifying: (6/10)x - (3/5)x + 12.
10. Combining like terms: (3/10)x + 12.
11. To find the percentage, we divide the number who did not participate by the total number and multiply by 100: [(3/10)x + 12] / x * 100.
12. Simplifying: (3/10) * 100 + (12 / x) * 100 = 30 + 120 / x.
a.) Therefore, the percentage of pupils in the art club who did not take part in the competition is 30 + 120 / x %.

13. To find the number of girls who did not participate in the competition, subtract the number who did participate in the competition from the total number of girls: (2/5)x - (1/10)x.
14. Simplifying: (4/10)x - (1/10)x = (3/10)x.
b.) Therefore, the number of girls who did not take part in the competition is (3/10)x.

Note: Without the exact value of "x," we cannot provide an exact numerical answer, but the above steps should give you the formulas to calculate the percentages and number of girls who did not participate in the competition.

To solve this problem, we will need to break it down into smaller steps. Let's start by calculating the number of girls and boys in the art club.

Step 1: Calculate the number of girls
Since 2/5 of the children in the art club were girls, we need to find 2/5 of the total number of children in the art club.
Let's assume the total number of children in the art club is x.
The number of girls would be (2/5) * x.

Step 2: Calculate the number of boys
To find the number of boys, subtract the number of girls from the total number of children in the art club.
Number of boys = Total number of children in the art club - Number of girls
Number of boys = x - (2/5) * x

Step 3: Calculate the number of girls who took part in the competition
Since 1/4 of the girls took part in the competition, we need to find 1/4 of the number of girls.
Number of girls who took part = (1/4) * (2/5) * x

Step 4: Calculate the number of boys who took part in the competition
Since 5/6 of the boys took part in the competition, we need to find 5/6 of the number of boys.
Number of boys who took part = (5/6) * (x - (2/5) * x)

Step 5: Calculate the total number of children who took part in the competition
Total number of children who took part = Number of girls who took part + Number of boys who took part

Step 6: Calculate the number of children who did not take part in the competition
Number of children who did not take part = Total number of children in the art club - Total number of children who took part

Now let's solve the problem using the given information:

a.) What percentage of the pupils in the art club did not take part in the competition?
Percentage of children who did not take part = (Number of children who did not take part / Total number of children in the art club) * 100

b.) How many girls did not take part in the competition?
Number of girls who did not take part = (2/5) * x - (1/4) * (2/5) * x

By substituting values into these formulas, you should be able to calculate the answers.