There 168 students in a school. There are twice as many girls as there are boys.
a) Calculate the number of girls in the school.
b) the students are to be divided
into seven classes so that each class has the same number of girls and boys.
i) calculate the number of girls and the number of boys in each class.
c) Apples are sold in boxes each containing 1 dozen.
i) how many boxes will the teacher have to buy so that each student receives one apple.
168 = 3*56 = 2*56 + 56
so, there are 112 girls and 56 boys
56 = 7*8
I think the rest is not so hard, right?
is part c 2 boxes
huh? 2 boxes is 2*12 = 24 apples
Think that's enough?
a) To calculate the number of girls in the school, we need to find out the ratio of girls to boys. We are given that there are twice as many girls as there are boys. Let's assign a variable to represent the number of boys, so let's say the number of boys is "x."
Since there are twice as many girls as boys, the number of girls would be 2x.
Now, we can set up an equation to solve for x:
x + 2x = 168
Combining like terms, we have:
3x = 168
Dividing both sides of the equation by 3, we get:
x = 56
Therefore, there are 56 boys in the school.
To find the number of girls, we substitute x into the equation:
2x = 2 * 56 = 112
Hence, there are 112 girls in the school.
b) To divide the students into seven classes with each class having the same number of girls and boys, we need to find a common factor of both the number of girls (112) and the number of boys (56).
The greatest common divisor (GCD) of 112 and 56 is 56.
To find the number of girls and boys in each class, we divide the total number of girls and boys by the common factor (56):
Number of girls in each class = 112 / 56 = 2 girls per class
Number of boys in each class = 56 / 56 = 1 boy per class
So, there will be 2 girls and 1 boy in each of the seven classes.
c) Since each student needs to receive one apple, and there are 168 students in the school, the teacher needs to buy enough apples for each student.
As given, apples are sold in boxes each containing 1 dozen (12 apples in one box).
To calculate the number of boxes required, we divide the total number of apples needed by the number of apples in one box:
Number of boxes needed = Total number of apples / Number of apples in one box
Total number of apples = Number of students = 168
Number of apples in one box = 12
Number of boxes needed = 168 / 12 = 14 boxes
Therefore, the teacher needs to buy 14 boxes so that each student receives one apple.