Welcome to the article A shop sells packs of black pens red pens and green pens There are 3 pens in each pack of black pens There are 5. On this page, you will learn the essential and logical steps to better understand the topic being discussed. We hope the information provided helps you gain valuable insights and is easy to follow. Let’s begin the discussion!
Answer :
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.
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.
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Rewritten by : Brahmana