Question

Ginny the gymnast has won gold and silver medals for her accomplishments. For every 4 gold medals won, she won 3 silver medals.
At this rate, if she won 12 gold medals, she will have received silver medals.
Question 2

Part B
If Ginny won 28 medals at the end of the season, she earned gold medals and silver medals

Answer 1

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**.