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Answer :
To determine which scenario is accurately modeled by the equation [tex]\((x)(0.65) = \$ 36.48\)[/tex], let's break down the statement of the equation:
1. The equation [tex]\((x)(0.65) = \$ 36.48\)[/tex] implies that when you multiply the value of [tex]\(x\)[/tex] by 0.65, you get \[tex]$36.48.
2. This means that 65% of the value \(x\) is equal to \$[/tex]36.48.
Now, let's interpret what [tex]\(x\)[/tex] represents:
- If 65% of something (the original price) is \[tex]$36.48, then \(x\) must be the original price of the boots.
- The equation shows that the boots are currently selling for 65% of their original cost, which results in the price of \$[/tex]36.48 during the sale. Therefore, [tex]\(x\)[/tex] is the original price before the discount.
Reviewing the scenarios given:
1. "A pair of boots is on sale for 65 percent of the original cost. The sale price of the boots is [tex]\(x, \$ 56.12\)[/tex]": Here, [tex]\(x\)[/tex] is incorrectly described as the sale price, and the number presented (\[tex]$56.12) does not match the calculation for the original price needed by the equation.
2. "A pair of boots is on sale for 35 percent of the original cost. The sale price of the boots is \(x, \$[/tex] 56.12\)": This contradicts the 65% in the equation and misrepresents what [tex]\(x\)[/tex] stands for.
3. "A pair of boots is on sale for 65 percent of the original cost. The original price of the boots is [tex]\(x, \$ 56.12\)[/tex]": This correctly states that [tex]\(x\)[/tex] is the original price, and the boots are on sale for 65% of that price.
4. "A pair of boots is on sale for 35 percent of the original cost. The original price of the boots is [tex]\(x, \$ 56.12\)[/tex]": This contradicts the 65% in the equation.
Based on the breakdown of the equation, the scenario that matches is:
A pair of boots is on sale for 65 percent of the original cost. The original price of the boots is [tex]\(x, \$ 56.12\)[/tex].
This description aligns with the situation described by the equation where [tex]\(x\)[/tex] is the original cost, and 65% of this original cost equals \$36.48.
1. The equation [tex]\((x)(0.65) = \$ 36.48\)[/tex] implies that when you multiply the value of [tex]\(x\)[/tex] by 0.65, you get \[tex]$36.48.
2. This means that 65% of the value \(x\) is equal to \$[/tex]36.48.
Now, let's interpret what [tex]\(x\)[/tex] represents:
- If 65% of something (the original price) is \[tex]$36.48, then \(x\) must be the original price of the boots.
- The equation shows that the boots are currently selling for 65% of their original cost, which results in the price of \$[/tex]36.48 during the sale. Therefore, [tex]\(x\)[/tex] is the original price before the discount.
Reviewing the scenarios given:
1. "A pair of boots is on sale for 65 percent of the original cost. The sale price of the boots is [tex]\(x, \$ 56.12\)[/tex]": Here, [tex]\(x\)[/tex] is incorrectly described as the sale price, and the number presented (\[tex]$56.12) does not match the calculation for the original price needed by the equation.
2. "A pair of boots is on sale for 35 percent of the original cost. The sale price of the boots is \(x, \$[/tex] 56.12\)": This contradicts the 65% in the equation and misrepresents what [tex]\(x\)[/tex] stands for.
3. "A pair of boots is on sale for 65 percent of the original cost. The original price of the boots is [tex]\(x, \$ 56.12\)[/tex]": This correctly states that [tex]\(x\)[/tex] is the original price, and the boots are on sale for 65% of that price.
4. "A pair of boots is on sale for 35 percent of the original cost. The original price of the boots is [tex]\(x, \$ 56.12\)[/tex]": This contradicts the 65% in the equation.
Based on the breakdown of the equation, the scenario that matches is:
A pair of boots is on sale for 65 percent of the original cost. The original price of the boots is [tex]\(x, \$ 56.12\)[/tex].
This description aligns with the situation described by the equation where [tex]\(x\)[/tex] is the original cost, and 65% of this original cost equals \$36.48.
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