1. **State the problem:** We have a bag with green, red, and blue marbles. The number of marbles for each color is given by expressions involving $x$ and $y$: - Green: $4x - y + 3$ - Red: $x + 3y - 5$ - Blue: $x + y + 11$ We know the probability of picking a green marble is $\frac{1}{5}$ and $x=3$. We need to find $y$. 2. **Write the formula for probability:** $$\text{Probability of green} = \frac{\text{Number of green marbles}}{\text{Total number of marbles}} = \frac{1}{5}$$ 3. **Substitute the expressions and $x=3$:** Number of green marbles: $$4(3) - y + 3 = 12 - y + 3 = 15 - y$$ Number of red marbles: $$3 + 3y - 5 = 3 + 3y - 5 = 3y - 2$$ Number of blue marbles: $$3 + y + 11 = y + 14$$ Total marbles: $$ (15 - y) + (3y - 2) + (y + 14) = 15 - y + 3y - 2 + y + 14 = (15 - 2 + 14) + (-y + 3y + y) = 27 + 3y$$ 4. **Set up the probability equation:** $$\frac{15 - y}{27 + 3y} = \frac{1}{5}$$ 5. **Cross multiply and solve for $y$:** $$5(15 - y) = 1(27 + 3y)$$ $$75 - 5y = 27 + 3y$$ $$75 - 27 = 3y + 5y$$ $$48 = 8y$$ $$y = \frac{48}{8} = 6$$ 6. **Final answer:** $$y = 6$$ This means when $x=3$, the value of $y$ that satisfies the probability condition is 6.