Calculate

In one class, each of the 30 students speaks either English or German. Three of them speak both languages. Those who speak only German outnumber those who speak only English by three.

Using a Venn diagram, calculate:
How many students speak English?
How many students speak only English?
How many students speak German?
How many students speak only German?

Final Answer:

a =  15
A =  12
n =  18
N =  15

Step-by-step explanation:

$$\begin{gathered} n=30=18 \\ a\cap n=3 \\ N=3+A \\ N+a\cap n+A=30 \\ (3+A)+3+A=30 \\ 2A=24 \\ A=\frac{24}{2}=12 \\ A=12 \\ N=3+A=3+12=15 \\ n=N+3=15+3=18 \\ a=A+3=12+3=15 \end{gathered}$$

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