1. **State the problem:** We have 59 balls in total, divided into green, emerald, and maroon colors. 2. **Define variables:** Let $g$ be the number of green balls, $e$ the number of emerald balls, and $m$ the number of maroon balls. 3. **Write the equations based on the problem:** - Total balls: $$g + e + m = 59$$ - Emerald balls are 4 fewer than green balls: $$e = g - 4$$ - Maroon balls are a quarter as many as green balls: $$m = \frac{g}{4}$$ 4. **Substitute $e$ and $m$ into the total balls equation:** $$g + (g - 4) + \frac{g}{4} = 59$$ 5. **Combine like terms:** $$g + g - 4 + \frac{g}{4} = 59$$ $$2g + \frac{g}{4} - 4 = 59$$ 6. **Add 4 to both sides:** $$2g + \frac{g}{4} = 59 + 4$$ $$2g + \frac{g}{4} = 63$$ 7. **Express $2g$ as $\frac{8g}{4}$ to combine terms:** $$\frac{8g}{4} + \frac{g}{4} = 63$$ $$\frac{9g}{4} = 63$$ 8. **Multiply both sides by 4 to clear the denominator:** $$\cancel{\frac{9g}{\cancel{4}}} \times 4 = 63 \times 4$$ $$9g = 252$$ 9. **Divide both sides by 9 to solve for $g$:** $$\frac{\cancel{9}g}{\cancel{9}} = \frac{252}{9}$$ $$g = 28$$ 10. **Find $e$ and $m$ using $g=28$:** $$e = g - 4 = 28 - 4 = 24$$ $$m = \frac{g}{4} = \frac{28}{4} = 7$$ 11. **Check the total:** $$28 + 24 + 7 = 59$$ which matches the total number of balls. **Final answer:** - Green balls: 28 - Emerald balls: 24 - Maroon balls: 7