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A bag contains 4 blue, 5 green and 3 red marbles. How many green marbles must be added to the bag so that at least 79 percent of the marbles are green?

Oct 17, 2020

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suppose you add $$x$$ green marbles

$$\dfrac{green}{total} = \dfrac{5 + x}{4 + 3 + 5 + x} = \dfrac{5 + x}{12 + x} = 0.79$$

multiply both sides by $$12 + x$$

$$5 + x = 9.48 + 0.79x$$

$$0.21x = 4.48$$

$$x = 21.\overline{3}$$

You need to add at least $$21.\overline{3}$$ green marbles, but that doesnt make sense here, since you can't have a fractional amount.

Rounding up, at least $$22$$ green marbles must be added

Oct 17, 2020