Answer :
Sure! Let's break down the given information and find out which scenario matches with the equation [tex]\((x)(0.65) = \$ 36.48\)[/tex].
The equation [tex]\((x)(0.65) = \$ 36.48\)[/tex] means that 65% of some original price, which we'll call [tex]\(x\)[/tex], results in a price of \[tex]$36.48.
Here's how we can interpret it:
1. Understand the equation:
- \((x)(0.65) = \$[/tex] 36.48\) means that you take the original price [tex]\(x\)[/tex], and find 65% of that price, which equals \[tex]$36.48.
2. Define the scenario:
- Since 65% of the original price equals \$[/tex]36.48, this indicates that the boots are on sale for 65% of their original cost. This means that \[tex]$36.48 is the sale price after the discount is applied.
3. Determine the unknown:
- The unknown in the equation is the original price \(x\) of the boots.
4. Solve for \(x\):
- To find \(x\), divide \$[/tex]36.48 by 0.65 to get the original price of the boots.
- [tex]\[ x = \frac{\$36.48}{0.65} \][/tex]
- This calculation gives us an original price of approximately \[tex]$56.12.
Given this analysis, 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 \(x, \$[/tex] 56.12\)."
This scenario accurately reflects the relationship described by the equation, identifying [tex]\(x\)[/tex] as the original price of the boots before the discount was applied.
The equation [tex]\((x)(0.65) = \$ 36.48\)[/tex] means that 65% of some original price, which we'll call [tex]\(x\)[/tex], results in a price of \[tex]$36.48.
Here's how we can interpret it:
1. Understand the equation:
- \((x)(0.65) = \$[/tex] 36.48\) means that you take the original price [tex]\(x\)[/tex], and find 65% of that price, which equals \[tex]$36.48.
2. Define the scenario:
- Since 65% of the original price equals \$[/tex]36.48, this indicates that the boots are on sale for 65% of their original cost. This means that \[tex]$36.48 is the sale price after the discount is applied.
3. Determine the unknown:
- The unknown in the equation is the original price \(x\) of the boots.
4. Solve for \(x\):
- To find \(x\), divide \$[/tex]36.48 by 0.65 to get the original price of the boots.
- [tex]\[ x = \frac{\$36.48}{0.65} \][/tex]
- This calculation gives us an original price of approximately \[tex]$56.12.
Given this analysis, 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 \(x, \$[/tex] 56.12\)."
This scenario accurately reflects the relationship described by the equation, identifying [tex]\(x\)[/tex] as the original price of the boots before the discount was applied.
