https://file.aiquickdraw.com/mathbot/file/1727034006281wot06lsm.jpg

The text extracted from the image is a bit incomplete, but the main details are clear:

- Yaqub has a bag containing only green and yellow pins.
- Initially, \(\frac{3}{7}\) of the pins are green.
- He picks out a green pin and gives it to his sister.
- After that, \(\frac{2}{5}\) of the remaining pins are green.

The question asks how many of the remaining pins are green and how many are yellow.

### Let’s solve it step-by-step:

1. Let \( x \) be the total number of pins in the bag initially.
2. The number of green pins initially is \( \frac{3}{7} \times x = \frac{3x}{7} \).
3. He gives away one green pin, so the remaining green pins are \( \frac{3x}{7} - 1 \).
4. The remaining total number of pins after giving away one pin is \( x - 1 \).
5. We are told that \(\frac{2}{5}\) of the remaining pins are green, so:
   \[
   \frac{2}{5} \times (x - 1) = \frac{3x}{7} - 1
   \]
6. Solve this equation for \( x \).

Let's compute this.The total number of pins in the bag initially is \( x = 21 \).

Now, let's calculate the number of green and yellow pins remaining in the bag:

1. Initially, the number of green pins is \( \frac{3}{7} \times 21 = 9 \).
2. After giving away 1 green pin, the remaining green pins are \( 9 - 1 = 8 \).
3. The remaining total number of pins is \( 21 - 1 = 20 \).
4. Of these 20 remaining pins, \(\frac{2}{5} \times 20 = 8\) are green.

Thus, the remaining pins are:
- **8 green pins**,
- The rest, \( 20 - 8 = 12 \), are **yellow pins**.

Would you like more details or have any questions?

Here are five related questions to explore further:
1. What fraction of the remaining pins are yellow?
2. How would the solution change if Yaqub gave away a yellow pin instead?
3. What if there were 30 total pins initially—how would that impact the numbers?
4. How would the situation change if the remaining fraction of green pins was \(\frac{3}{5}\)?
5. Can you derive a general formula for any initial fraction of green pins?

**Tip:** When solving word problems, translate the situation into equations step by step to keep the problem manageable.

Yaqub has a bag only containing green and yellow pins. 3/7 of the pins are green. He picks out a green pin from his bag and gives it to his sister. 2/5 of the remaining pins in his bag are green. How many of the remaining pins in his bag are green and how many are yellow?

Learn how to solve a problem involving fractions of green and yellow pins in a bag. Yaqub initially has 3/7 green pins. After removing one, 2/5 of the remaining pins are green. This problem covers key algebraic and proportional concepts.

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