In a class, 2/7 of the pupils are girls. 1/2 of the girls and 1/3 of the boys in the class wear glasses. If 10 boys wear glasses, how many of the girls wear glasses?
total number of students ---- x
number of girls = (2/7)x
number of boys = (5/7)x
number of girls with glasses = (1/2)(2/7)x = (1/7)x
number of boys with glasses = (1/3)(5/7)x = (5/21)x
given: (5/21)x = 10
solve for x, and sub into my definition
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Let's break down the problem step by step.
Step 1: Calculate the number of girls in the class.
If 2/7 of the pupils are girls, we need to multiply the total number of pupils by 2/7.
Let's assume the total number of pupils in the class is "x".
The number of girls in the class is (2/7) * x.
Step 2: Calculate the number of boys in the class.
Since the total number of pupils in the class is "x", we can subtract the number of girls from the total to find the number of boys.
The number of boys in the class is x - (2/7) * x.
Step 3: Calculate the number of boys who wear glasses.
If 1/3 of the boys wear glasses, we need to multiply the number of boys by 1/3.
The number of boys who wear glasses is (1/3) * (x - (2/7) * x).
Step 4: Set up an equation using the given information.
We know that 10 boys wear glasses, so we can set up the equation:
(1/3) * (x - (2/7) * x) = 10.
Step 5: Solve the equation for x.
To solve for x, we can multiply both sides of the equation by 3 to eliminate the fraction:
x - (2/7) * x = 30.
Next, we can multiply both sides by 7 to remove the fraction:
7x - 2x = 210.
Simplifying, we get:
5x = 210.
Dividing both sides by 5, we find:
x = 42.
Therefore, there are 42 pupils in the class.
Step 6: Calculate the number of girls who wear glasses.
Since we found that there are 42 pupils in the class, we can substitute this value into the equation for the number of girls: (2/7) * 42.
Calculating, we get:
(2/7) * 42 = 12.
Therefore, 12 girls in the class wear glasses.
To find out how many girls wear glasses, we need to determine the total number of boys and girls in the class and then calculate the proportion of girls who wear glasses.
Let's start by finding the total number of boys in the class. We know that 10 boys wear glasses, and the proportion of boys who wear glasses is 1/3. So, we can set up the following equation:
(1/3) * Total number of boys = 10
To isolate the total number of boys, we can multiply both sides of the equation by 3:
Total number of boys = 10 * 3
Total number of boys = 30
Now, let's determine the total number of pupils in the class. We know that 2/7 of the pupils are girls. So, we can set up the following equation:
(2/7) * Total number of pupils = Total number of girls
To find the total number of pupils, we can multiply both sides of the equation by 7/2:
Total number of pupils = Total number of girls * (7/2)
Total number of pupils = Total number of girls * 7/2
Total number of pupils = 30
Now, we can solve for the total number of girls:
Total number of girls * (7/2) = 30
To isolate the total number of girls, we can multiply both sides of the equation by 2/7:
Total number of girls = 30 * 2/7
Total number of girls = 60/7
Since the number of girls must be a whole number, we need to round the result. In this case, the closest whole number is 9.
So, there are 9 girls in the class. Since 1/2 of the girls wear glasses, we can calculate the number of girls who wear glasses:
Number of girls wearing glasses = (1/2) * Total number of girls wearing glasses
Number of girls wearing glasses = (1/2) * 9
Number of girls wearing glasses = 4.5
Again, we need to round to the nearest whole number. In this case, 4 girls wear glasses.
Therefore, 4 girls in the class wear glasses.