Answer :
To determine which scenario is modeled by the equation [tex]\((x)(0.65) = \$ 36.48\)[/tex], we need to understand what this equation represents. The equation shows that 65% of the original price [tex]\(x\)[/tex] is equal to \[tex]$36.48, which is likely the sale price.
Let's break it down step-by-step:
1. Identifying the Equation:
\((x)(0.65) = \$[/tex] 36.48\) suggests that the sale price of the boots is 65% of the original price.
2. Solving for [tex]\(x\)[/tex]:
To find the original price of the boots (represented by [tex]\(x\)[/tex]), we can rearrange the equation:
[tex]\[
x = \frac{36.48}{0.65}
\][/tex]
By calculating this, we find that:
[tex]\[
x \approx 56.12
\][/tex]
3. Matching the Scenario:
The equation solved to find [tex]\(x\)[/tex] (approximately \[tex]$56.12) suggests this is the original price of the boots, with 65% being the sale price.
Considering the options:
- "A pair of boots is on sale for 65 percent of the original cost. The sale price of the boots is \(x, \$[/tex] 56.12\)" suggests the original pricing.
- "A pair of boots is on sale for 35 percent of the original cost. The sale price of the boots is [tex]\(x, \$ 56.12\)[/tex]" doesn't fit as the equation shows a 65% sale price.
- "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]" is the correct scenario because the calculation supports this.
- "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]" also doesn't fit because the discount percentage should be 65%.
Thus, the scenario that matches the equation [tex]\((x)(0.65) = \$ 36.48\)[/tex] 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]."
Let's break it down step-by-step:
1. Identifying the Equation:
\((x)(0.65) = \$[/tex] 36.48\) suggests that the sale price of the boots is 65% of the original price.
2. Solving for [tex]\(x\)[/tex]:
To find the original price of the boots (represented by [tex]\(x\)[/tex]), we can rearrange the equation:
[tex]\[
x = \frac{36.48}{0.65}
\][/tex]
By calculating this, we find that:
[tex]\[
x \approx 56.12
\][/tex]
3. Matching the Scenario:
The equation solved to find [tex]\(x\)[/tex] (approximately \[tex]$56.12) suggests this is the original price of the boots, with 65% being the sale price.
Considering the options:
- "A pair of boots is on sale for 65 percent of the original cost. The sale price of the boots is \(x, \$[/tex] 56.12\)" suggests the original pricing.
- "A pair of boots is on sale for 35 percent of the original cost. The sale price of the boots is [tex]\(x, \$ 56.12\)[/tex]" doesn't fit as the equation shows a 65% sale price.
- "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]" is the correct scenario because the calculation supports this.
- "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]" also doesn't fit because the discount percentage should be 65%.
Thus, the scenario that matches the equation [tex]\((x)(0.65) = \$ 36.48\)[/tex] 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]."
