Welcome to the article A shop sells packs of black pens packs of red pens and packs of green pens There are 2 pens in each pack of black. 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 :
The correct answer is the number of green pens sold was 11220, calculated by considering the ratio of packs sold and the number of pens in each pack, resulting in a total of 212 pens sold.
To find out the number of green pens sold, let's first calculate the total number of packs sold for each color.
Given the ratio of black to red to green packs sold is 7:3:4, we can express it as fractions of the total packs sold:
Black packs: [tex]\( \frac{7}{7+3+4} = \frac{7}{14} \)[/tex] of the total packs
Red packs: [tex]\( \frac{3}{7+3+4} = \frac{3}{14} \)[/tex] of the total packs
Green packs: [tex]\( \frac{4}{7+3+4} = \frac{4}{14} \)[/tex] of the total packs
Now, let's find the total number of pens sold for each color:
Black pens: [tex]\( 2 \times \frac{7}{14} \times \text{total pens} \)[/tex]
Red pens: [tex]\( 5 \times \frac{3}{14} \times \text{total pens} \)[/tex]
Green pens: [tex]\( 6 \times \frac{4}{14} \times \text{total pens} \)[/tex]
Given that the total number of pens sold is 212, we can set up the equation:
[tex]\[ 2 \times \frac{7}{14} \times 212 + 5 \times \frac{3}{14} \times 212 + 6 \times \frac{4}{14} \times 212 = 212 \][/tex]
Solving this equation will give us the number of green pens sold.
Let's solve this equation:
[tex]\[ 2 \times \frac{7}{14} \times 212 + 5 \times \frac{3}{14} \times 212 + 6 \times \frac{4}{14} \times 212 \][/tex]
[tex]\[ = 2 \times \frac{7}{14} \times 212 + 5 \times \frac{3}{14} \times 212 + 6 \times \frac{4}{14} \times 212 \][/tex]
[tex]\[ = 2 \times \frac{7}{14} \times 212 + 5 \times \frac{3}{14} \times 212 + 6 \times \frac{4}{14} \times 212 \][/tex]
[tex]\[ = 2 \times 7 \times 212 + 5 \times 3 \times 212 + 6 \times 4 \times 212 \][/tex]
[tex]\[ = 2 \times 7 \times 212 + 5 \times 3 \times 212 + 6 \times 4 \times 212 \][/tex]
[tex]\[ = 2 \times 7 \times 212 + 5 \times 3 \times 212 + 6 \times 4 \times 212 \][/tex]
[tex]\[ = 2968 + 3180 + 5072 \][/tex]
[tex]\[ = 11220 \][/tex]
So, 11220 green pens were sold.
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Rewritten by : Brahmana
The number of green pens sold was found by setting up an equation using the given pen pack ratio and the total pens sold. Solving this, we found that 96 green pens were sold.
To work out the number of green pens sold, we need to use the ratio of packs sold and the number of pens in each pack to set up an equation.
Let's define variables for the number of packs of black, red, and green pens sold as B, R, and G respectively. According to the given ratio Black: Red: Green = 7 : 3 : 4, we can express the number of packs as B = 7x, R = 3x, G = 4x, where x is a common multiple.
The total number of pens sold by the shop can be represented as:
2 pens per pack of black pens (2 * 7x packs) = 14x pens
5 pens per pack of red pens (5 * 3x packs) = 15x pens
6 pens per pack of green pens (6 * 4x packs) = 24x pens
Adding these up gives the total number of pens sold:
14x + 15x + 24x = 53x
We know that a total of 212 pens were sold:
53x = 212
Solving for x, we get:
x = 212 / 53 = 4
Now we substitute x back into the equation for the number of green pens:
6 pens per pack (6* 4x) = 96 green pens
Therefore, the number of green pens sold was 96.