To solve the problem, we first need to find out how many silver medals Ginny earned if she won 12 gold medals.
Part A: Finding Silver Medals for 12 Gold Medals
We know from the rate provided that for every 4 gold medals, she won 3 silver medals. This can be represented as a ratio:
\[ \text{Gold : Silver} = 4 : 3 \]
If she won 12 gold medals, we can find out how many silver medals she won by setting up a proportion:
\[ \frac{4 \text{ gold}}{3 \text{ silver}} = \frac{12 \text{ gold}}{x \text{ silver}} \]
Cross-multiplying to solve for \( x \):
\[ 4x = 12 \times 3 \]
\[ 4x = 36 \]
\[ x = \frac{36}{4} = 9 \]
So, if Ginny won 12 gold medals, she won 9 silver medals.
Part B: Total Medals and Breakdown
Ginny earned a total of 28 medals. We need to keep the same ratio of gold to silver medals.
Given the ratio \( \text{Gold : Silver} = 4 : 3 \), we can express the total number of medals in terms of \( x \), where \( x \) is a multiplier for the ratio:
Let \( 4x \) be the number of gold medals and \( 3x \) be the number of silver medals.
\[ 4x + 3x = 28 \]
\[ 7x = 28 \]
Dividing both sides by 7 gives:
\[ x = 4 \]
Now we can find the number of gold and silver medals:
Gold Medals: \[ 4x = 4 \times 4 = 16 \]
Silver Medals: \[ 3x = 3 \times 4 = 12 \]
Thus, at the end of the season, Ginny earned 16 gold medals and 12 silver medals.