Answer :
- The equation $(x)(0.65) = $36.48$ represents 65% of $x$ equals $36.48.
- Scenario 1 and 2 state the sale price is $x$, which doesn't match the equation.
- Scenario 4 states the boots are on sale for 35% off, which doesn't match the equation.
- Scenario 3 states the original price is $x$ and the sale is 65% off, matching the equation. Therefore, the answer is $\boxed{C}$.
### Explanation
1. Understanding the Problem
We are given the equation $(x)(0.65) = $36.48$ and four scenarios. We need to determine which scenario is modeled by the equation. The equation means that 65% of some value $x$ is equal to $36.48.
2. Analyzing Each Scenario
Let's analyze each scenario:
Scenario 1: A pair of boots is on sale for 65 percent of the original cost. The sale price of the boots is $x, $56.12.
This means that 65% of the original cost is equal to the sale price $x$. So, $0.65 * (original\ cost) = x$. This does not match the equation $(x)(0.65) = $36.48$.
Scenario 2: A pair of boots is on sale for 35 percent of the original cost. The sale price of the boots is $x, $56.12.
This means that 35% of the original cost is equal to the sale price $x$. So, $0.35 * (original\ cost) = x$. This does not match the equation $(x)(0.65) = $36.48$.
Scenario 3: A pair of boots is on sale for 65 percent of the original cost. The original price of the boots is $x, $56.12.
This means that 65% of the original price $x$ is equal to the sale price. So, $0.65 * x = sale\ price$. If the sale price is $36.48, then $0.65 * x = $36.48$. This matches the equation $(x)(0.65) = $36.48$.
Scenario 4: A pair of boots is on sale for 35 percent of the original cost. The original price of the boots is $x, $56.12.
This means that 35% of the original price $x$ is equal to the sale price. So, $0.35 * x = sale\ price$. This does not match the equation $(x)(0.65) = $36.48$.
3. Conclusion
Therefore, scenario 3 is the correct one.
### Examples
Understanding percentages and how they relate to original prices and sale prices is crucial in everyday shopping. For example, if you want to buy a TV that's 30% off and originally costs $500, you can use this concept to calculate the sale price: $500 * 0.30 = $150 (discount), so the sale price is $500 - $150 = $350. This helps you make informed decisions and manage your budget effectively.
- Scenario 1 and 2 state the sale price is $x$, which doesn't match the equation.
- Scenario 4 states the boots are on sale for 35% off, which doesn't match the equation.
- Scenario 3 states the original price is $x$ and the sale is 65% off, matching the equation. Therefore, the answer is $\boxed{C}$.
### Explanation
1. Understanding the Problem
We are given the equation $(x)(0.65) = $36.48$ and four scenarios. We need to determine which scenario is modeled by the equation. The equation means that 65% of some value $x$ is equal to $36.48.
2. Analyzing Each Scenario
Let's analyze each scenario:
Scenario 1: A pair of boots is on sale for 65 percent of the original cost. The sale price of the boots is $x, $56.12.
This means that 65% of the original cost is equal to the sale price $x$. So, $0.65 * (original\ cost) = x$. This does not match the equation $(x)(0.65) = $36.48$.
Scenario 2: A pair of boots is on sale for 35 percent of the original cost. The sale price of the boots is $x, $56.12.
This means that 35% of the original cost is equal to the sale price $x$. So, $0.35 * (original\ cost) = x$. This does not match the equation $(x)(0.65) = $36.48$.
Scenario 3: A pair of boots is on sale for 65 percent of the original cost. The original price of the boots is $x, $56.12.
This means that 65% of the original price $x$ is equal to the sale price. So, $0.65 * x = sale\ price$. If the sale price is $36.48, then $0.65 * x = $36.48$. This matches the equation $(x)(0.65) = $36.48$.
Scenario 4: A pair of boots is on sale for 35 percent of the original cost. The original price of the boots is $x, $56.12.
This means that 35% of the original price $x$ is equal to the sale price. So, $0.35 * x = sale\ price$. This does not match the equation $(x)(0.65) = $36.48$.
3. Conclusion
Therefore, scenario 3 is the correct one.
### Examples
Understanding percentages and how they relate to original prices and sale prices is crucial in everyday shopping. For example, if you want to buy a TV that's 30% off and originally costs $500, you can use this concept to calculate the sale price: $500 * 0.30 = $150 (discount), so the sale price is $500 - $150 = $350. This helps you make informed decisions and manage your budget effectively.
