There are 42 pupils in a class. 3/4 of the boys and 2/3 of the girls travel to school by bus. The total number of boys and girls who travel to school by bus is 30.
(a) How many boys are there in the class?
(b) How many girls travel to school by bus?
X Boys in the class.
Y Girls in the class.
3x/4 + 2y/3 = 30,
Multiply by 12:
Eq1: 9x + 8y = 360.
x/4 + y/3 = 42-30 = 12,
Multiply by 12:
Eq2: 3x + 4y = 144.
Multiply Eq2 by -3 and add:
9x + 8y = 360
-9x - 12y = -432
Sum: -4y = -72, Y = 18.
3x + 4*18 = 144, X = 24.
What is the answer
Yes it is correct answer
total no of students =42
no of students coming by bus=30
no of boys coming by bus= 3/4*30 =22
no of girls coming by bus =2/3*30 =20
so total =22+20
=42 total ..
To solve this problem, we'll need to set up some equations based on the given information.
Let's denote the number of boys in the class as "B" and the number of girls as "G".
From the first piece of information, we know that there are a total of 42 pupils in the class. Therefore, B + G = 42 (equation 1).
Given that 3/4 of the boys and 2/3 of the girls travel to school by bus, we can write the following equation:
(3/4)B + (2/3)G = 30 (equation 2).
We can solve these two equations simultaneously to find the values of B and G.
To eliminate fractions, we can multiply equation 2 by the least common multiple (LCM) of 4 and 3, which is 12. This gives us:
9B + 8G = 360 (equation 3).
Now, we can solve equations 1 and 3 simultaneously. One way to do this is by using the method of substitution.
From equation 1, we have B = 42 - G.
Substituting this value of B into equation 3, we get:
9(42 - G) + 8G = 360.
Expanding and simplifying, we get:
378 - 9G + 8G = 360.
Combining like terms, we have:
-G = 360 - 378.
Simplifying further, we get:
-G = -18.
To solve for G, we can multiply both sides of the equation by -1, which gives:
G = 18.
Now, substitute the value of G back into equation 1 to find the number of boys:
B + 18 = 42.
Subtracting 18 from both sides, we get:
B = 42 - 18.
Simplifying, we find:
B = 24.
Therefore, there are 24 boys in the class (answer to part a), and since 2/3 of the girls travel by bus, we can calculate the number of girls who travel by bus as follows:
(2/3)G = (2/3)(18) = 12.
Hence, 12 girls travel to school by bus (answer to part b).