3/4of the girls in sssq play basketball and 4/7 play volleyball . every girl plays at least one of these games.if 27 girls play both games , how many girls are there in the class
Let's assume that there are a total of x girls in the class.
According to the given information, 3/4 of the girls play basketball. So, the number of girls playing basketball is 3/4 * x.
Similarly, 4/7 of the girls play volleyball. So, the number of girls playing volleyball is 4/7 * x.
Since every girl plays at least one of these games, we can add the two numbers above to get the total number of girls who play either basketball or volleyball.
Number of girls playing either basketball or volleyball = 3/4 * x + 4/7 * x
Now, we are given that 27 girls play both games. So, we need to subtract this number from the total number of girls playing either basketball or volleyball.
Total number of girls playing either basketball or volleyball - Number of girls playing both games = x
(3/4 * x + 4/7 * x) - 27 = x
Multiplying both sides of the equation by 28 to clear the fractions:
21x + 16x - 756 = 28x
37x - 756 = 28x
Subtracting 28x and adding 756 to both sides of the equation:
37x - 28x = 756
9x = 756
Dividing both sides of the equation by 9:
x = 756 / 9
x = 84
Therefore, there are 84 girls in the class.
Let's assume the total number of girls in the class is represented by "x".
According to the given information, 3/4 of the girls play basketball, and 4/7 play volleyball. This means that 3/4 of x girls play basketball, and 4/7 of x girls play volleyball.
We also know that every girl plays at least one of these games.
To find the total number of girls in the class, we can sum up the number of girls who play basketball and the number of girls who play volleyball.
Number of girls who play basketball = 3/4 * x
Number of girls who play volleyball = 4/7 * x
Now, we need to subtract the 27 girls who play both games since we counted them twice.
Total number of girls who play either basketball or volleyball = (3/4 * x) + (4/7 * x) - 27
Since every girl plays at least one of the games, this total should be equal to the total number of girls in the class.
Therefore, we can set up the equation:
(3/4 * x) + (4/7 * x) - 27 = x
To solve this equation, we first need to find a common denominator for 4/7 and 3/4, which is 28.
Multiplying and simplifying, the equation becomes:
(21x + 16x)/28 - 27 = x
(37x - 756)/28 = x
37x - 756 = 28x
9x = 756
x = 84
Therefore, there are 84 girls in the class.
To find the total number of girls in the class, we need to add the number of girls who play basketball and the number of girls who play volleyball and then subtract the number of girls who play both games.
Let's denote the total number of girls in the class as "x".
According to the given information:
3/4 of the girls play basketball, which means (3/4) * x.
4/7 of the girls play volleyball, which means (4/7) * x.
We know that every girl plays at least one game, so adding these two fractions together should give us the total number of girls, while taking into account that 27 girls play both games.
So the equation becomes:
(3/4) * x + (4/7) * x - 27 = x
Now, let's solve this equation to find the value of x.
First, we need to get rid of the fractions by finding a common denominator. In this case, the least common denominator is 28.
(21/28) * x + (16/28) * x - 27 = x
Next, we can simplify the equation by multiplying through by 28 to eliminate the denominators:
21x + 16x - 756 = 28x
Combine like terms:
37x - 756 = 28x
Now, solve for x:
37x - 28x = 756
9x = 756
x = 756 / 9
x = <<756/9=84>>84
Hence, there are 84 girls in the class.