Answer:
Let the number of pounds sold for each type of pastry be $x$. Then the income from each type of pastry can be expressed as $0.50x$, $0.70x$, and $0.90x$, respectively.
The total income from the sales is given as $252$, so we can set up an equation:
$$0.50x + 0.70x + 0.90x = 252$$
Simplifying this equation, we get:
$$2.10x = 252$$
Dividing both sides by $2.10$, we get:
$$x = 120$$
Therefore, each type of pastry sold $120$ pounds, and the total number of pounds sold is $3 \times 120 = 360$ pounds.
So the answer is (E) 36 pounds