B. Originally planned to spend 1500 yuan to buy $x$ pieces of product A and $y$ pieces of product B, but the price of product A increased by 1.5 yuan per piece, and the price of product B increased by 1 yuan per piece. Despite buying 10 fewer pieces of product A, the total amount was still 29 yuan more. If the price of both products increased by only 1 yuan per piece, and the number of pieces of product A purchased was only 5 less than originally planned, then the total amount paid for products A and B would be 1563.5 yuan.
(1) Find the relationship between $x$ and $y$;
(2) If twice the number of pieces of product A originally planned to be purchased plus the number of pieces of product B originally planned to be purchased is greater than 205 but less than 210, find the number of pieces of product A and product B originally planned to be purchased.
B. (1) Let the original planned unit prices for goods A and B be $a$ yuan and $b$ yuan, respectively. Then the original plan is
$$
a x + b y = 1500 \text{. }
$$

When the unit price of good A increases by 1.5 yuan, the unit price of good B increases by 1 yuan, and the quantity of good A decreases by 10 units, we get
$$
(a + 1.5)(x - 10) + (b + 1) y = 1529. \text{ (2) }
$$

When the unit price of good A increases by 1 yuan, the quantity of good A is 5 units less than the original plan, and the unit price of good B increases by 1 yuan, we get
$$
(a + 1)(x - 5) + (b + 1) y = 1563.5 \text{. }
$$
(2) - (1) and (3) - (2) respectively yield
$$
\begin{array}{l}
1.5 x + y - 10 a = 44, \\
x + y - 5 a = 68.5 .
\end{array}
$$

Thus, $x + 2 y = 186$.
(2) According to the problem, we have
$$
205 < 2 x + y < 210 \text{. }
$$

From $2 x + y = 2(186 - 2 y) + y = 372 - 3 y$, we know $205 < 372 - 3 y < 210$
$$
\Rightarrow 54 < y < 55 \frac{2}{3} \text{. }
$$

Since $y$ is an integer, we get $y = 55$.
Thus, $x = 186 - 2 \times 55 = 76$.
Therefore, the original plan was to purchase 76 units of good A and 55 units of good B.