To analyze the equation \( (x)(0.6) = 86.46 \) and determine which scenario it represents, we can break down the components of the equation:
- Let \( x \) represent an original price. The term \( (x)(0.6) \) indicates that we are calculating 60 percent of the original price \( x \).
- The right side of the equation, \( 86.46 \), is the amount that this 60 percent represents.
From this, we can infer that \( 86.46 \) is 60 percent of the original price \( x \). To find the original price, we can rearrange the equation:
\[ x = \frac{86.46}{0.6} \]
This means that the picnic table is being sold for 60 percent of its original price, and the price \( 86.46 \) reflects that 60 percent.
Thus, the correct scenario is:
A picnic table is on sale for 60 percent off, and the sale price of the picnic table is \( x = 86.46 \). The original price of the picnic table would be \( 144.10 \).
This aligns with the third scenario provided:
A picnic table is on sale for 60 percent off. The original price of the picnic table is \( x, 144.10 \).