Question

a survey of students at a university shows that 4 out of 5 drink coffee. of the students who drink coffee, 1 out of 8 adds cream to it. if the university has 32,000 students, find the number of students who drink coffee with cream. how many students drink coffee with cream? \boxed{} students

Explanation:

Step1: Calculate the number of coffee - drinking students

The proportion of coffee - drinking students is \(\frac{4}{5}\). The total number of students is \(N = 32000\).
The number of coffee - drinking students \(n_1\) is \(n_1=\frac{4}{5}\times32000\).

$$n_1=\frac{4\times32000}{5}=4\times6400 = 25600$$

Step2: Calculate the number of students who drink coffee with cream

The proportion of coffee - drinking students who add cream is \(\frac{1}{8}\). Let \(n_1 = 25600\) (the number of coffee - drinking students).
The number of students who drink coffee with cream \(n_2\) is \(n_2=\frac{1}{8}\times n_1\).
Substitute \(n_1 = 25600\) into the formula: \(n_2=\frac{1}{8}\times25600\)

$$n_2=\frac{25600}{8}=3200$$

Answer:

\(3200\)