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Answer :
To solve the problem and identify the correct scenario using the given equation [tex]\((x)(0.65) = \$ 36.48\)[/tex], let's think through the problem:
1. Understanding the Equation:
- The equation [tex]\(x \times 0.65 = 36.48\)[/tex] implies that [tex]\(0.65\)[/tex] represents 65% of some original amount, [tex]\(x\)[/tex]. This means that 65% of the original price results in the sale price of \[tex]$36.48.
2. Interpreting the Equation:
- From the equation, we know that \$[/tex]36.48 is the sale price after applying the 65% rate. Therefore, [tex]\(x\)[/tex] must be the original price of the boots before the discount was applied.
3. Identifying the Correct Scenario:
- Let's examine each option to see which one matches:
- Option 1: The sale price is \[tex]$56.12, but the equation shows the sale price is \$[/tex]36.48, so this is incorrect.
- Option 2: This states a 35% discount, but our equation uses a 65% discount, so this is incorrect.
- Option 3: This option states that the boots are on sale for 65% of the original cost and asks for the original price, which matches our equation [tex]\((x)(0.65) = 36.48\)[/tex].
- Option 4: This again mentions a 35% discount, which does not align with our equation.
4. Conclusion:
- The correct scenario is the third one: "A pair of boots is on sale for 65 percent of the original cost. The original price of the boots is [tex]\(x\)[/tex]."
So, based on the information and verifying the match with the equation, the correct scenario is: "A pair of boots is on sale for 65 percent of the original cost. The original price of the boots is [tex]\(x\)[/tex]."
1. Understanding the Equation:
- The equation [tex]\(x \times 0.65 = 36.48\)[/tex] implies that [tex]\(0.65\)[/tex] represents 65% of some original amount, [tex]\(x\)[/tex]. This means that 65% of the original price results in the sale price of \[tex]$36.48.
2. Interpreting the Equation:
- From the equation, we know that \$[/tex]36.48 is the sale price after applying the 65% rate. Therefore, [tex]\(x\)[/tex] must be the original price of the boots before the discount was applied.
3. Identifying the Correct Scenario:
- Let's examine each option to see which one matches:
- Option 1: The sale price is \[tex]$56.12, but the equation shows the sale price is \$[/tex]36.48, so this is incorrect.
- Option 2: This states a 35% discount, but our equation uses a 65% discount, so this is incorrect.
- Option 3: This option states that the boots are on sale for 65% of the original cost and asks for the original price, which matches our equation [tex]\((x)(0.65) = 36.48\)[/tex].
- Option 4: This again mentions a 35% discount, which does not align with our equation.
4. Conclusion:
- The correct scenario is the third one: "A pair of boots is on sale for 65 percent of the original cost. The original price of the boots is [tex]\(x\)[/tex]."
So, based on the information and verifying the match with the equation, the correct scenario is: "A pair of boots is on sale for 65 percent of the original cost. The original price of the boots is [tex]\(x\)[/tex]."
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