There are 42 student 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 come to school by bus is 30. How many boys are there in the class?
To solve this problem, we can use algebra. Let's assume the number of boys in the class is 'x'.
According to the given information, 3/4 of the boys and 2/3 of the girls travel to school by bus. So, the number of boys who come to school by bus is (3/4)x, and the number of girls who come to school by bus is (2/3)(42-x), since the total number of students in the class is 42.
The question states that the total number of boys and girls who come to school by bus is 30. So, we can set up the equation:
(3/4)x + (2/3)(42-x) = 30
To simplify the equation, we can multiply through by the common denominator, which is 12:
9x + 8(42-x) = 360
Simplifying further:
9x + 336 - 8x = 360
Combine like terms:
x + 336 = 360
Subtract 336 from both sides:
x = 24
Therefore, there are 24 boys in the class.
b+g=42
3/4 b + 2/3 g = 30
g = 42-b, so
3/4 b + 2/3 (42-b) = 30
b = 24