Half of the students in Sonia's class are girls. Half of the girls have brown hair. Half of the brown haired girls have brown eyes. There are 4 girls with brown hair and brown eyes. How many students are in Sonia's class?
(1/2)(1/2)(1/2)n = 4
1/8n = 4
n = 4 / (1/8)
n = 4 * (8/1)
n = ?
32 students in Sonia's class
Right.
Work backwards from four and use the halves.
To determine the number of students in Sonia's class, we can start by looking at the information provided.
Let's denote:
G = total number of girls in the class
B = total number of students with brown hair
E = total number of students with brown eyes
According to the given information, we know that:
1. Half of the students in the class are girls, which means G = (1/2) * total number of students.
2. Half of the girls have brown hair, so B = (1/2) * G.
3. Half of the brown-haired girls have brown eyes, so E = (1/2) * B.
We also know that there are 4 girls with both brown hair and brown eyes, which means that the number of girls with brown hair and brown eyes is 4.
From point 2 above, we can substitute the value of B in terms of G:
B = (1/2) * G.
From point 3 above, we can substitute the value of E in terms of B:
E = (1/2) * B = (1/2) * ((1/2) * G) = (1/4) * G.
Now, we can set up an equation using the given information:
(1/4) * G = 4.
To solve for G, we can multiply both sides of the equation by 4:
G = 4 * 4 = 16.
So, there are 16 total students in Sonia's class.