in a class, 3/5 of the girls and 1/6 of the boys wear spectacles. If 3/4 of those who are wearing spectacles are girls, what fraction of the pupils does not wear spectacles?
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To find the fraction of pupils who do not wear spectacles, we need to first determine the fraction of boys and girls who wear spectacles and then subtract that from 1.
Let's denote:
- G: total number of girls in the class
- B: total number of boys in the class
- SG: number of girls who wear spectacles
- SB: number of boys who wear spectacles
We are given the following information:
- 3/5 of the girls wear spectacles: SG = (3/5)G
- 1/6 of the boys wear spectacles: SB = (1/6)B
- 3/4 of those who wear spectacles are girls: SG = (3/4)(SG + SB)
To solve for the unknown variables, we can set up a system of equations based on the above information:
From the first piece of information, we have:
SG = (3/5)G
From the second piece of information, we have:
SB = (1/6)B
From the third piece of information, we have:
SG = (3/4)(SG + SB)
Now, substituting the values of SG and SB from the first two equations into the third equation, we get:
(3/5)G = (3/4)((3/5)G + (1/6)B)
To find the fraction of pupils who do not wear spectacles, we need to subtract the fraction who wear spectacles from 1. So, the fraction of pupils who do not wear spectacles is:
1 - ((SG + SB)/(G + B))
Now, we can solve the equations to find the values of G and B. Once we have those values, we can substitute them into the above equation to find the fraction of pupils who do not wear spectacles.