Let's start by breaking down the information given in the problem:
1. Number of pens per pack:
- Each pack of black pens contains 3 pens.
- Each pack of red pens contains 5 pens.
- Each pack of green pens contains 6 pens.
2. Ratio of packs sold:
- The ratio of black pen packs sold to red pen packs sold to green pen packs sold is given as 7:2:4.
3. Total number of pens sold:
- A total of 220 pens were sold.
Next, let's determine how many packs of each type were sold based on the given ratio:
- The total parts of the ratio are [tex]\(7 + 2 + 4 = 13\)[/tex].
Now, to find out how many packs were sold in total, we can divide the total number of pens sold (220) by the number of pens per pack for the combined ratio:
[tex]\[
\begin{aligned}
\text{Total parts sold} &= \left(7 \times 3\right) + \left(2 \times 5\right) + \left(4 \times 6\right) \\
&= 21 + 10 + 24 \\
&= 55 \text{ pens (per unit ratio)}
\end{aligned}
\][/tex]
Now, we know that the total number of pens (220) corresponds to these 55 ratio parts. To find out the number of packs sold overall, we use:
[tex]\[
\text{Total packs sold} = \frac{220}{55} = 4
\][/tex]
Since the packs sold follow the ratio 7:2:4, we can calculate the number of green pen packs sold:
[tex]\[
\text{Number of green pen packs sold} = 4 \times 4 = 16
\][/tex]
Finally, since each pack of green pens contains 6 pens:
[tex]\[
\text{Number of green pens sold} = 16 \times 6 = 96
\][/tex]
Hence, 96 green pens were sold.
