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From B2: b. is too kind a grader. I would've docked you all for not showing your work. spoilers

There are 13 red balls and 30 non-red balls.
Proportion of red balls = 13/(13+30) = 13/43

Let x = the number of red balls added to the jar.
Proportion of red balls now = P = (13+x)/(43+x).

Require P >= 2/3.
(13+x)/(43+x) >= 2/3.
3*(13+x) >= 2*(43+x).
39 + 3x >= 86 + 2x
x >= 47.


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