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There are 180 girls in a kindergarten and the number of girls is 20% more than that of boys.
(a) Find the number of boys in the kindergarten. XX\1+90%) =180
(b) If 84% of the boys and 40% of the girls come from the mainland, find the percentage of mainland students in the kindergarten. 180X46% + aX84%
(2 marks)
(2 marks)
180 + a
(c) It is known that 10 boys and 20 girls have left the kindergarten (i Find the percentage of girls in the kindergarten.
. 80-10 X 100%
180
(ii) If now the number of boys is ×% less than that of girls, find the value of x.
Bot GPT 3.5
answered
(a) Let's assume the number of boys in the kindergarten is x. According to the given information, the number of girls is 20% more than that of boys, which can be expressed as:
Number of girls = x + 20% of x = x + 0.2x = 1.2x
We are given that the total number of girls in the kindergarten is 180. So we can set up the equation:
1.2x = 180
Dividing both sides by 1.2:
x = 150
So the number of boys in the kindergarten is 150.
(b) We need to find the percentage of mainland students in the kindergarten. We know that 84% of the boys and 40% of the girls come from the mainland.
Number of boys from mainland = 84% of boys = 84/100 * 150 = 126
Number of girls from mainland = 40% of girls = 40/100 * 180 = 72
Total number of mainland students = 126 + 72 = 198
The percentage of mainland students in the kindergarten is:
198/180 * 100% = 110%
(c) (i) After 10 boys and 20 girls leave the kindergarten, the new number of girls in the kindergarten will be:
180 - 20 = 160
The percentage of girls in the kindergarten is:
160/180 * 100% = 88.89%
(ii) We are given that the number of boys is ×% less than that of girls. Let's assume the value of x is the percentage of boys less than girls.
Number of boys = 160 * (1 - x/100) (as the number of boys is ×% less than that of girls)
Number of girls = 160
From part (a), we know that the number of girls was 180 initially. Using the same logic, we get:
160 = (180 - 10) * (1 - x/100)
160 = 170 * (1 - x/100)
160/170 = 1 - x/100
0.9412 = 1 - x/100
x/100 = 1 - 0.9412
x/100 = 0.0588
x = 5.88
So the value of x is 5.88. Therefore, the number of boys is 5.88% less than that of girls.