Answer :
Let's break down the problem step by step to understand which scenario is modeled by the equation [tex]\( (x)(0.65) = \$36.48 \)[/tex].
1. Understanding the Equation:
- The equation [tex]\( (x)(0.65) = \$36.48 \)[/tex] tells us that after applying a 65% factor to some original price [tex]\( x \)[/tex], we get a final amount of \[tex]$36.48.
- This implies that \$[/tex]36.48 is the sale price after a discount that leaves the buyer paying 65% of the original price.
2. Solving for the Original Price [tex]\( x \)[/tex]:
- To find the original price [tex]\( x \)[/tex], you would rearrange the equation to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{36.48}{0.65}
\][/tex]
3. Calculate the Original Price:
- Carrying out this division, you find that the original price [tex]\( x \)[/tex] is approximately \[tex]$56.12.
4. Matching the Scenario:
- Since the equation shows that the sale price after paying 65% of the original is \$[/tex]36.48 and the original price was determined to be approximately \[tex]$56.12, we need to find the scenario that matches this description.
- The scenario where a pair of boots is on sale for 65 percent of the original cost, and the original price of the boots is \( x \), matches our findings.
Therefore, 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 \( x, \$[/tex]56.12 \).
1. Understanding the Equation:
- The equation [tex]\( (x)(0.65) = \$36.48 \)[/tex] tells us that after applying a 65% factor to some original price [tex]\( x \)[/tex], we get a final amount of \[tex]$36.48.
- This implies that \$[/tex]36.48 is the sale price after a discount that leaves the buyer paying 65% of the original price.
2. Solving for the Original Price [tex]\( x \)[/tex]:
- To find the original price [tex]\( x \)[/tex], you would rearrange the equation to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{36.48}{0.65}
\][/tex]
3. Calculate the Original Price:
- Carrying out this division, you find that the original price [tex]\( x \)[/tex] is approximately \[tex]$56.12.
4. Matching the Scenario:
- Since the equation shows that the sale price after paying 65% of the original is \$[/tex]36.48 and the original price was determined to be approximately \[tex]$56.12, we need to find the scenario that matches this description.
- The scenario where a pair of boots is on sale for 65 percent of the original cost, and the original price of the boots is \( x \), matches our findings.
Therefore, 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 \( x, \$[/tex]56.12 \).
