In a class of 52 students 16 study science.1/3 of boys and 1/4 of girls. How many boys are in the class.
"1/3 of boys and 1/4 of girls." is not a complete sentence.
What about the 1/3 of boys and 1/4 of girls ?
To find the number of boys in the class, we need to first determine the number of students studying science.
We are given that 16 students study science, and this number represents 1/3 of the total number of boys plus 1/4 of the total number of girls.
Let's assume the number of boys in the class is represented by 'b' and the number of girls by 'g'.
According to the given information, the equation for the number of students studying science can be written as:
16 = (1/3) * b + (1/4) * g
Since we are trying to find the number of boys and not the number of girls, we need to eliminate the variable 'g' from the equation.
We also know that the total number of students in the class is 52, so we can write an equation representing the total number of students:
52 = b + g
To eliminate the variable 'g', we can solve the second equation for 'g' and substitute it into the first equation.
g = 52 - b
Substituting this value of 'g' into the first equation, we can solve for 'b':
16 = (1/3) * b + (1/4) * (52 - b)
Multiplying through by 12 (the least common multiple of 3 and 4) to eliminate the fractions, we get:
192 = 4b + (3) * (52 - b)
192 = 4b + 156 - 3b
Combining like terms, we have:
192 - 156 = 4b - 3b
36 = b
Therefore, there are 36 boys in the class.