Question

which scenario is modeled by the equation (x)(0.65) = $36.48?
a pair of boots is on sale for 65 percent of the original cost. the sale price of the boots is x, $56.12.
a pair of boots is on sale for 65 percent of the original cost. the original price of the boots is x, $56.12.
a pair of boots is on sale for 35 percent of the original cost. the sale price of the boots is x, $56.12.
a pair of boots is on sale for 35 percent of the original cost. the original price of the boots is x, $56.12.

Explanation:

Step1: Analyze the equation meaning

The equation is \((x)(0.65)=\$36.48\) (assuming a typo and the right - hand side is \(\$36.48\) or similar, but from the options, we focus on the percentage interpretation). A coefficient of \(0.65\) means \(65\%\) of the original price \(x\) gives the sale price. So if the sale price is \(x\times0.65\), it means the boots are on sale for \(65\%\) of the original cost (since \(100\% - 35\%=65\%\), which is a \(35\%\) discount, and we pay \(65\%\) of the original price). Also, the structure of the equation is original price \(x\) times \(0.65\) equals the sale price. So we need to check which option has the original price as \(x\), on sale for \(65\%\) of original cost, and the sale price related correctly. Looking at the options, the option "A pair of boots is on sale for 65 percent of the original cost. The original price of the boots is \(x\), \(\$56.12\)" (assuming the sale price calculation: if \(x = 56.12\), then \(56.12\times0.65 = 36.478\approx36.48\)) fits. The other options with \(35\%\) would have a coefficient of \(0.35\) in the equation, not \(0.65\). And the options where the sale price is \(x\) are incorrect because the equation has \(x\) (original price) times \(0.65\) as sale price.

Step2: Match with options

We eliminate options with \(35\%\) (since the coefficient is \(0.65\) not \(0.35\)) and options where the sale price is \(x\) (since the equation is original price \(x\) times \(0.65\) equals sale price). So the correct option is the one where a pair of boots is on sale for 65 percent of the original cost and the original price is \(x\), \(\$56.12\) (the option: "A pair of boots is on sale for 65 percent of the original cost. The original price of the boots is \(x\), \(\$56.12\)").

Answer:

A pair of boots is on sale for 65 percent of the original cost. The original price of the boots is \(x\), \(\$56.12\) (the corresponding option among the given ones, e.g., if the option is labeled as the second one from the left or with the relevant text as above)