1. The percentage of boys in a math circle, rounded to an integer, is equal to 51%. The percentage
of girls in this math circle, rounded to an integer, is equal to 49%. What is the minimal possible
number of participants in the circle?pl properly answer
Answers
Given : The percentage of boys in a math circle, rounded to an integer, is equal to 51%. The percentage of girls in this math circle, rounded to an integer, is equal to 49%
To Find : What is the minimal possible number of participants in the circle?
Solution:
minimal possible number of participants in the circle
if B = G + 1
Total = B + G
= G + 1 + G
= 2G + 1
Girls Percentage = 100G/(2G + 1)
rounded to an integer, is equal to 49%
48.5 ≤ 100G/(2G + 1) < 49.5
=> 97G + 48.5 ≤ 100G < 99G + 49.5
=> 48.5 ≤ 3G => 16.16 ≤ G < 49.5
G = 17
G + 1 = 18
17 + 18 = 35
minimal possible number of participants in the circle = 35
or we can solve by Boys percentage
Boys percentage = 100 (G + 1)/ (2G + 1)
rounded to an integer, is equal to 51%
50.5 ≤ 100(G+1)/(2G + 1) < 51.5
=> 101G + 50.5 ≤ 100G + 100 < 103G + 51.5
G ≤ 49.5
3G > 48.5 => G > 16.16
Girls = 17
Boys = 18
Total = 35
Girls % = ( 17/35) * 100 = 48.57 = 49 %
Boys % = ( 18/35) * 100 = 51.43 = 51 %
minimal possible number of participants in the circle = 35
Another Ways Difference between 48.5 and 51.5 is less than 3% greater than 1 %
3 % = 1
Hence > 33
34 is even so difference of one is not possible
so 35 Total
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The percentage of boys in a math circle,
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