An alloy contains p% silver by weight. A 100-gram piece of the alloy is added to it. After this, the new alloy is found to contain 90% silver by weight. If another 90-gram piece is added, the new alloy contains 84% silver by weight. Find the weight of the initial alloy.

Let the weight of the initial alloy be x, with p% silver by weight.

For the first condition:

(px + 100 * 3) / (x + 3) = 90

90(x + 3) = px + 300

90x + 270 = px + 300

px = 90x - 30

p = 90 - (30 / x)

For the second condition:

(px + 90 * 2) / (x + 2) = 84

84(x + 2) = px + 180

84x + 168 = px + 180

px = 84x - 12

Substituting p = 90 - (30 / x):

(90 - 30 / x)x = 84x - 12

90x - 30 = 84x - 12

6x = 18 → x = 3

Answer: 3 kg.