Problem 424

Since $21$ pieces of fruit are
not apples, then the number of pears added to the number of bananas is
$21$.

Since $25$ pieces of fruit are not
pears, then the number of apples added to the number of bananas is $25$.

Since $28$ pieces of fruit are not
bananas, then the number of apples added to the number of pears is $28$.

In adding these three totals $21+25+28$, we are counting the number of
pears twice, the number of bananas twice, and the number of apples twice
(since each appears in exactly two of the three statements above).

That is, $21+25+28=74$ is twice the
total number of pieces of fruit, and so the number of pieces of fruit in
the box is $\frac{74}{2}=37$.