3/4 of the girls in SS1 play basketball and 4/7 play volleyball every girl needs at least one of these games if 27 girls play both games how many girls are there in the class
3/4-27+27+4/7-27=x
Solve for x
Let's break down the information given step-by-step to solve the problem:
1. Let's assume the total number of girls in the class is x.
2. According to the given information, 3/4 of the girls play basketball. So, the number of girls playing basketball is 3/4 * x = 3x/4.
3. Additionally, 4/7 of the girls play volleyball. So, the number of girls playing volleyball is 4/7 * x = 4x/7.
4. The question states that every girl needs to play at least one of the games. Therefore, the total number of girls playing basketball or volleyball is given by: (3x/4) + (4x/7).
5. Since 27 girls play both games, we need to subtract the double-counted girls from the total: [(3x/4) + (4x/7)] - 27 = (21x + 16x - 756)/(28) = 37x/28 - 756/28.
6. We know that the total number of girls playing at least one game is equal to the total number of girls in the class, x. So, we can set up an equation to solve for x: (37x/28) - (756/28) = x.
7. Simplifying the equation, we have: 37x - 756 = 28x.
8. Solving for x, we subtract 28x from both sides of the equation: 37x - 28x - 756 = 0.
9. Combining like terms, we have: 9x - 756 = 0.
10. To isolate x, we add 756 to both sides of the equation: 9x = 756.
11. Lastly, we divide both sides of the equation by 9: x = 756/9.
Therefore, there are 84 girls in the class.
To solve this problem, we will use a method called the intersecting sets method.
Let's denote:
- G as the number of girls who play basketball
- V as the number of girls who play volleyball
- B as the number of girls who play both basketball and volleyball
From the given information, we know that 3/4 of the girls play basketball, so we can write it as an equation: G = (3/4) * T, where T is the total number of girls in the class.
Similarly, we know that 4/7 of the girls play volleyball, so another equation can be written as: V = (4/7) * T.
We also know that 27 girls play both games, so we can write it as: B = 27.
According to the problem, every girl needs to play at least one game, so the total number of girls in the class is the sum of girls who play basketball only (G - B), girls who play volleyball only (V - B), and girls who play both basketball and volleyball (B).
Therefore, the equation becomes: T = (G - B) + (V - B) + B
Simplifying this equation, we get: T = G + V - B
Now we can substitute the values we know into the equation to find the number of girls in the class:
T = (3/4) * T + (4/7) * T - 27
Multiplying the fractions by their respective denominators, we have:
T = (21/28) * T + (16/28) * T - 27
Combining like terms, we get:
T = (37/28) * T - 27
Let's isolate the variable T:
T - (37/28) * T = -27
(28/28) * T - (37/28) * T = -27
(28 - 37) / 28 * T = -27
-9/28 * T = -27
Multiplying both sides by -28/9, we have:
T = (-27) * (-28/9)
T = 84
Therefore, there are 84 girls in the class.
3/4 x + 4/7 x - 27 = x
now just solve for x