## 31. Child Psychology

The brightest hours of a little child are spent drawing. He depicts either Indians or Eskimos and draws a dwelling for each of them. Thus, next to the Eskimos, he usually draws an igloo, and next to the Indians - wigwams. But sometimes the child makes mistakes, and not infrequently, for example, an igloo can be found next to the Indians. One female psychologist took these drawings very seriously; she discovered that there were twice as many Indians as Eskimos, that there were as many Eskimos with wigwams as there were Indians with igloos, and that, speaking of Eskimos, one wigwam corresponds to three igloos. Then she decided to determine what part of the inhabitants of the wigwams are Indians (and derive from this a very complex IQ $^{1}$ formula for the child). But she has not yet succeeded in doing so. Help her.
31. Let $E W$ be the fraction of drawings depicting an Eskimo and a wigwam, $E I$ be the fraction of drawings depicting an Eskimo and an igloo, $I I$ be the fraction of drawings depicting Indians and an igloo, and finally, $I W$ be the fraction of drawings depicting Indians and a wigwam. Then the following equalities hold:

$$
\begin{gathered}
E W+E I+I I+I W=1 \\
(I W+I I)=2(E W+E I) \\
I I=E W \\
E I=3 E W
\end{gathered}
$$

Substituting the last values of $I I$ and $E I$ into the first two equations, we get

$$
\begin{aligned}
& E W+3 E W+E W+I W=1 \\
& (I W+E W)=2(E W+3 E W)
\end{aligned}
$$

or

$$
\begin{aligned}
& 5 E W+I W=1 \\
& 7 E W-I W=0
\end{aligned}
$$

From this, we easily deduce

$$
E W=1 / 12, \quad I W=7 / 12
$$

The result that our psychologist is looking for is:

$$
\frac{I W}{I W+E W}=\frac{7}{12}: \frac{8}{12}=\frac{7}{8}
$$