安德鲁收集了金星、银星和铜星。他有100颗金星。他收集的星星中30%是银星。他的铜星比银星多12颗。

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 = $154 - 84 = 70$