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# Algebra

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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?

Jan 1, 2022

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22 green marbles.

To solve, let x be the number of marbles added.

$$\frac{5+x}{12+x}>\frac{79}{100}$$

simplifying, we see that

$$x>21\frac{1}{3}$$

so x is at least 22.

If we put this back into the original problem, there would be 27 green marbles and 34 marbles total.

27/34 is about 0.79411, which is slightly above 79%.

Jan 2, 2022