The area of Marley's patio is 96 yards²
Step-by-step explanation:
To solve the problem let us assume that
∵ Area of the old yard = length × width
∵ The length of the old yard = 100%
∵ The width of the old yard = 100%
∴ Area of the old yard = 100 × 100 = 10,000%
∵ The patio decreased the length of her yard by 15% and decreased
the width of her yard by 20%
∴ The length of the new yard = 100% - 15% = 85%
∴ The width of the new yard = 100% - 20% = 80%
∴ Area of the new yard = 85 × 80 = 6,800%
Now let us using the ratio to find the area of the old yard
∵ The area of the new yard is 204 yards²
→ Old area : New area
→ 10,000% : 6,800%
→ O.A : 204
By using cross multiplication
∴ O.A × 6,800% = 204 × 10,000%
- Divide both sides by 6,800%
∴ O.A = 300
- O.A represents the old area
∴ The old area = 300 yards²
∵ The area of Marley's patio is the difference between the old area
of the yard and the new area of the yard
∵ The old area of the yard = 300 yards²
∵ The new area of the yard = 204 yards²
∴ The area of the patio = 300 - 204 = 96 yards²
The area of Marley's patio is 96 yards²
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