3. There are three types of goods, A, B, and C. If you buy 3 pieces of A, 7 pieces of B, and 1 piece of C, it costs 3.15 yuan; if you buy 4 pieces of A, 10 pieces of B, and 1 piece of C, it costs 4.20 yuan. Now, buying 1 piece each of A, B, and C will cost $\qquad$ yuan.
3. 1.05 yuan

Let the cost of 1 item of product A be $x$ yuan, 1 item of product B be $y$ yuan, and 1 item of product C be $z$ yuan,

According to the problem, we have
$$
\left\{\begin{array}{c}
3 x+7 y+z=3.15, \\
4 x+10 y+z=4.20 .
\end{array}\right.
$$
(2) - (1), we get
$$
x+3 y=1.05 \text{. }
$$

Substituting (3) $\times 2$ into (1), we get
$$
x+y+z=1.05 \text{. }
$$

Therefore, the cost of purchasing one item each of A, B, and C is 1.05 yuan.