3/4 of the girls in SSS1 play basket ball 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?
3/4 x + 4/7 x - 27 = x
You may wish to start with a Venn diagram : )
That is two intersecting circles... where the overlap is the 27 that play both games.
20
To find the total number of girls in the class, we can use the concept of the inclusion-exclusion principle.
Let's denote the total number of girls in the class as 'x'.
According to the question,
- 3/4 of the girls play basketball. Therefore, the number of girls playing basketball is (3/4)x.
- 4/7 of the girls play volleyball. So, the number of girls playing volleyball is (4/7)x.
Since we know that every girl plays at least one of these games, we can add the number of girls playing basketball and the number of girls playing volleyball and then subtract the girls playing both games to avoid double counting.
[(3/4)x] + [(4/7)x] - 27 = x
To solve this equation, we can simplify it step by step:
Expand the fractions:
(3/4)x + (4/7)x - 27 = x
Multiply through by the least common multiple of the denominators (4 and 7) to eliminate the fractions:
(7/7)*(3/4)x + (4/4)*(4/7)x - 27 = (4/4)*x
Simplify:
(21/28)x + (16/28)x - 27 = x
Combine like terms:
(37/28)x - 27 = x
Move 'x' to one side and the constant term to the other side:
(37/28)x - x = 27
Simplify:
(37/28 - 1)x = 27
(9/28)x = 27
Now we can solve for 'x' by multiplying both sides by the reciprocal of (9/28), which is (28/9):
[(9/28)x] * (28/9) = 27 * (28/9)
Simplify:
x = (27 * 28) / 9
Calculate:
x = 84
Therefore, there are 84 girls in the class.