3/4 of the girls in a 3rd form class play netball and 4/7 play volleyball . Every girl plays atleast one of these games. If 27 play both games,how many girls are there in the 3rd form
let the total be x
make a Venn diagram of two intersecting circles, and place 27 in the intersection.
In the exclusive parts of the two circles place
(3/4)x - 27 and (4/7)x - 27
then:
(3/4)x-27 + 27 + (4/7)x-27 = x
(3/4)x + (4/7)x-27 = x
multiply each term by 28, the LCD
21x + 16x - 756 = 28x
9x=756
x = 84
THE 20 boy
Let's denote the total number of girls in the 3rd form as "x."
According to the given information:
- 3/4 of the girls play netball, which is (3/4) * x.
- 4/7 of the girls play volleyball, which is (4/7) * x.
- There are 27 girls who play both netball and volleyball.
To determine the total number of girls in the 3rd form, we need to add the number of girls who play netball and the number of girls who play volleyball, but we must subtract the 27 girls who play both from the sum.
Number of girls who play netball = (3/4) * x
Number of girls who play volleyball = (4/7) * x
Number of girls who play both = 27
Total number of girls in the 3rd form = (3/4) * x + (4/7) * x - 27
To simplify this expression, we need to find a common denominator for 4 and 7, which is 28.
Total number of girls in the 3rd form = (21/28) * x + (16/28) * x - 27
Combining the like terms, we get:
Total number of girls in the 3rd form = (37/28) * x - 27
Since the number of girls cannot be a fraction, we need to find a value for x that makes the fraction a whole number.
To determine this value, we check if 37 is divisible by 28.
37 ÷ 28 ≈ 1.3214
Since 37 is not divisible by 28, we need to find the closest whole number greater than 1.3214 that is divisible by 28.
By trial and error, we find that 56 is the smallest whole number greater than 1.3214 divisible by 28.
Now, substituting x = 56 into the expression:
Total number of girls in the 3rd form = (37/28) * 56 - 27
Total number of girls in the 3rd form ≈ 74.8571 - 27
Total number of girls in the 3rd form ≈ 47.8571
Rounding to the nearest whole number, we find that there are approximately 48 girls in the 3rd form.
To solve this problem, you can use the principle of inclusion-exclusion. Let's break down the information given:
We know that 3/4 of the girls play netball and 4/7 play volleyball. Let's denote the total number of girls in the 3rd form as 'x'.
The number of girls who play netball can be calculated as (3/4) * x, and the number of girls who play volleyball can be calculated as (4/7) * x.
However, we need to consider that there are 27 girls who play both games. If we add the number of netball players and the number of volleyball players, we would count these 27 girls twice. So, we need to subtract this overlap of 27 girls from the total count.
Now, let's calculate the number of girls who play netball: (3/4) * x.
Similarly, the number of girls who play volleyball: (4/7) * x.
Since every girl plays at least one of these games, the total number of girls can be calculated as:
(3/4) * x + (4/7) * x - 27 = x.
To solve this equation for 'x', we can first simplify the equation:
(21/28) * x + (16/28) * x - 27 = x.
(37/28) * x - 27 = x.
Now, let's isolate 'x' on one side of the equation:
(37/28) * x - x = 27.
(37/28 - 1) * x = 27.
7/28 * x = 27.
x = (27 * 28) / 7.
x = 108.
Therefore, there are 108 girls in the 3rd form.