A shop sells packs of black pens, packs of red pens and packs of green pens - Edexcel - GCSE Maths - Question 7 - 2019 - Paper 1

Similarly, for red pens: There are 5 pens in each pack of red pens.

Number of red pens sold = Number of packs of red pens sold × Pens per pack = 3 × 5 = 15 pens.

Next, for green pens: There are 6 pens in each pack of green pens and we denote the number of packs of green pens sold as 4.

So, the number of green pens sold = Number of packs of green pens sold × Pens per pack = 4 × 6 = 24 pens.

Now let's verify our calculations by summing the total number of pens sold:

Total pens sold = Number of black pens + Number of red pens + Number of green pens = 14 + 15 + 24 = 53 pens.

According to the problem, a total of 212 pens were sold, so the values associated with the respective number of packs must follow a ratio of 7:3:4. We can set up the equations:

Let the common ratio constant be x:

Number of black pens = 7x, Number of red pens = 3x, Number of green pens = 4x.

Since each pack has a specific number of pens, we need to sum these ratios times their respective counts of pens per pack:

Total pens = 2(7x) + 5(3x) + 6(4x) = 212.

Now we can deduce:

14x + 15x + 24x = 212,

53x = 212

=> x = (rac{212}{53}) = 4.

Substituting back for green pens sold:

Number of green pens sold = 4x × 6 = 96.