There are some pupils in the zoo. 2/5 of them are girls, of whom 20% of them do not wear caps. 2/3 of the boys do not wear caps. What is the percentage of the pupils in the zoo who wear caps?
pupils at zoo ---- x
girls at zoo = 2x/5
girls wearing caps = (20/100)(2x/5) = 2x/25
boys at zoo = 3x/5
boys wearing caps = (2/3)(3x/5) = 2x/5
total wearing caps = 2x/25 + 2x/5 = 12x/25
percentage wearing caps = (12x/25) / x
= 12/25 = .48
So 48% of students are wearing caps
because 20% of the girls don’t wear caps and 2/3 of the boys do not wear caps
So the percentage of the pupils who don’t wear caps is
2/5 * 20% + (1 - 2/5) * 2/5 = 2/25 + 2/5 = 48%
1 - 48% = 52%
of 52% of the pupils wear caps
To find the percentage of pupils in the zoo who wear caps, we need to determine the proportion of pupils who do not wear caps.
Let's break down the information given step by step:
1. We know that 2/5 of the pupils are girls. So, let's assume the total number of pupils in the zoo is 5x. Then, the number of girls is 2x.
2. Of these girls, 20% do not wear caps. To find out how many girls do not wear caps, we can calculate 20% of 2x: (20/100) * 2x = (1/10) * 2x = (1/5) * x = x/5.
3. We also know that 2/3 of the boys do not wear caps. Since the remaining pupils are boys, let's find out how many boys there are. The total number of pupils is 5x, and the number of girls is 2x. So, the number of boys is 5x - 2x = 3x.
4. Now, let's calculate how many boys do not wear caps. 2/3 of the boys do not wear caps, so the number of boys who do not wear caps is (2/3) * 3x = 2x.
5. Adding the number of girls and boys who do not wear caps, we get x/5 + 2x = (x + 10x)/5 = 11x/5.
6. To determine the proportion of pupils who do wear caps, we need to subtract the proportion of pupils who do not wear caps from 1. So, 1 - (11x/5)/(5x) = 1 - (11/25) = 25/25 - 11/25 = 14/25.
7. Finally, to find the percentage, we need to multiply the proportion by 100. So, the percentage of pupils in the zoo who wear caps is (14/25) * 100 = 56%.
Therefore, the percentage of pupils in the zoo who wear caps is 56%.