for every girl taking classes at the school, there are 3 boys who are taking classes at the school. If there are 236 students taking classes, write and solve a propotion to predict the number of boys taking classes at the school.
3/4 = x/236
Cross multiply and solve for x.
X=177
To write a proportion to predict the number of boys taking classes at the school, we will compare the ratio of girls to boys in the given information to the actual number of students.
Let's assume the number of girls taking classes is represented by "x". According to the information, for every girl, there are 3 boys taking classes. So, the number of boys will be 3 times the number of girls, which is 3x.
The total number of students taking classes is given as 236. This includes both girls and boys.
Therefore, we can set up the proportion:
x (number of girls) : 3x (number of boys) = 236 (total number of students) : x + 3x
Simplifying the proportion:
x : 3x = 236 : 4x
To solve the proportion, we cross multiply:
236 * 3x = 4x * x
708x = 4x^2
Now, let's solve the quadratic equation to find the value of x:
4x^2 - 708x = 0
Factor out common terms:
4x(x - 177) = 0
Setting each factor equal to zero:
4x = 0 -> x = 0 (not possible in this context)
x - 177 = 0 -> x = 177
Since the number of girls cannot be zero, we choose the positive value, x = 177.
Therefore, there are 177 girls and the number of boys can be found by multiplying by 3:
Number of boys = 3 * x = 3 * 177 = 531
Thus, the predicted number of boys taking classes at the school is 531.