Marley turned part of her yard into a patio. This patio decreased the length of her yard by 15% and decreased the width of her yard by 20%. The area of her yard is now 204 square yards. What is the area of Marley’s patio?
Let's assume the original length of the yard is L and the original width is W.
The area of the yard is then L * W.
After turning part of her yard into a patio, the new length of the yard is 0.85L (decreased by 15%) and the new width is 0.8W (decreased by 20%).
The new area of the yard is now 0.85L * 0.8W = 0.68LW (the area of the yard decreased by 32%).
Since the new area of the yard is 204 square yards, we can write the equation: 0.68LW = 204.
Dividing both sides of the equation by 0.68 gives us LW = 300.
Now, we are asked to find the area of Marley’s patio, which is the difference between the original area of the yard and the new area of the yard: L*W - 0.68*L*W.
Factoring out the common term, we have L*W * (1 - 0.68).
Simplifying, we find the area of Marley's patio is 0.32 * L * W.
Since we know the original area of the yard is LW = 300, the area of Marley's patio is 0.32 * 300 = 96 square yards. Answer: \boxed{96}.