Andrew had a collection of gold, silver and bronze stars. He had 100 gold stars. 30% of his collection was silver stars. He had 12 more bronze stars than silver stars.

1. Express the total percentage of the collection in terms of the given parts to find the value of a percentage unit.

Let the total number of stars be $100\%$.
Silver stars = $30\%$
Bronze stars = $30\% + 12$
Gold stars = $100$

Total = Silver + Bronze + Gold
$100\% = 30\% + (30\% + 12) + 100$
$100\% = 60\% + 112$
$40\% = 112$

2. Find the total number of gold and bronze stars using complementary percentage.

Percentage of gold and bronze stars = $100\% - 30\% \text{ (silver)} = 70\%$

Since $40\% = 112$,
$10\% = 112 \div 4 = 28$
$70\% = 28 \times 7 = 196$

Total number of gold and bronze stars is $196$.

1. Find the initial number of silver stars and the total number of gold and bronze stars

From part (a), the initial total number of stars is $280$.
Initial number of silver stars = $30\% \times 280 = 84$
Total number of gold and bronze stars = $280 - 84 = 196$

2. Find the new number of silver stars using the unchanged quantity

The number of gold and bronze stars remains unchanged at $196$.
New percentage of silver stars = $44\%$
New percentage of gold and bronze stars = $100\% - 44\% = 56\%$
$56\%$ of the new total corresponds to $196$ stars.
New number of silver stars ($44\%$) = $\frac{196}{56} \times 44 = 154$

3. Calculate the number of silver stars received

Number of silver stars received = $154 - 84 = 70$