Mathematical Reasoning Puzzle

#167

You are running a small business. To promote your brand, you decided to distribute Red, Black and Green Pens (having your brand name on them) among 100 persons. You have a budget of 100 dollars.
You decided not buy a single pen extra and also spending the exact $100 on buying pens. (Expecting printing cost nil)
The cost of different colored pens i.e Red, Black and Green Pens are $6, $3 ad $0.10 respectively.
So, what is the exact number of different colored pens will you buy ?

  Difficulty Level - 5/5

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  Solution : 

   Let "R", "B" and "G" be the number of Red, Black and Green Pens. We know two equations:
           R +   B +        G = 100                                       --- 1
        6R + 3B + 0.1G = 100                                --- 2
By multiplying the first equation by 6 and then 3 >>
        6R + 6B + 6G = 600
        3R + 3B + 3G = 300
Subtracting these two equations from the second, we can come up with two more equations:
                  3B = 500 - 5.9G
                  3R = 2.9G - 200 
Normally, two equations isn't enough to solve for three variables. 
But R,B and G are non-negative integers. 
So, if 3B ≥ 0, then 500 - 5.9G ≥ 0. This means G ≤ 84.75. 
Also, if 3R ≥ 0, then 2.9G - 200 ≥ 0. This means G ≥ 68.97.
i.e only two numbers can be possible which are 70 & 80.(as pens can't be fractional)
>>>> If G=80, then, R=10.67, and B=9.33. But R and B must be integers, so, it is not the solution.

>>>> If G=70, then, R=1, and B=29.

So, 1 Red Pen must be bought for $6.00, 29 Black Pens must be bought for $87.00, and 
70 Green Pens must be bought for $7.00.