Answer :
To solve the given problem, we need to understand which scenario matches the equation [tex]\( (x)(0.65) = 3648 \)[/tex].
The equation [tex]\( (x)(0.65) = 3648 \)[/tex] can be interpreted as finding an original price, [tex]\( x \)[/tex], which, when multiplied by 65% (or 0.65), results in [tex]$3648.
To find \( x \), the original price of the boots, we divide 3648 by 0.65:
1. Understand the Equation: The equation means 65% of \( x \) equals $[/tex]3648.
2. Solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{3648}{0.65}
\][/tex]
3. Calculate [tex]\( x \)[/tex]:
[tex]\[
x \approx 5612.3077
\][/tex]
This calculation shows that [tex]\( x \)[/tex], or the original price of the boots, is approximately [tex]$5612.31.
Now, let's identify which scenario the equation models:
- The key here is that multiplying by 0.65 implies you are calculating 65% of the original price.
- Therefore, \( x \) represents the original price of the boots, not the sale price.
Let's match this with the given options:
1. Option A: A pair of boots is on sale for 65 percent of the original cost. The sale price of the boots is $[/tex]x, [tex]$56.12.
2. Option B: A pair of boots is on sale for 35 percent of the original cost. The sale price of the boots is $[/tex]x, [tex]$56.12.
3. Option C: A pair of boots is on sale for 65 percent of the original cost. The original price of the boots is $[/tex]x, [tex]$56.12.
4. Option D: A pair of boots is on sale for 35 percent of the original cost. The original price of the boots is $[/tex]x, [tex]$56.12.
The correct scenario is:
- Option C: A pair of boots is on sale for 65 percent of the original cost. The original price of the boots is $[/tex]x, [tex]$56.12.
Option C accurately describes the situation: the original price is $[/tex]x, and after applying the 65% sale factor, the result is $3648. The equation represents this scenario correctly.
The equation [tex]\( (x)(0.65) = 3648 \)[/tex] can be interpreted as finding an original price, [tex]\( x \)[/tex], which, when multiplied by 65% (or 0.65), results in [tex]$3648.
To find \( x \), the original price of the boots, we divide 3648 by 0.65:
1. Understand the Equation: The equation means 65% of \( x \) equals $[/tex]3648.
2. Solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{3648}{0.65}
\][/tex]
3. Calculate [tex]\( x \)[/tex]:
[tex]\[
x \approx 5612.3077
\][/tex]
This calculation shows that [tex]\( x \)[/tex], or the original price of the boots, is approximately [tex]$5612.31.
Now, let's identify which scenario the equation models:
- The key here is that multiplying by 0.65 implies you are calculating 65% of the original price.
- Therefore, \( x \) represents the original price of the boots, not the sale price.
Let's match this with the given options:
1. Option A: A pair of boots is on sale for 65 percent of the original cost. The sale price of the boots is $[/tex]x, [tex]$56.12.
2. Option B: A pair of boots is on sale for 35 percent of the original cost. The sale price of the boots is $[/tex]x, [tex]$56.12.
3. Option C: A pair of boots is on sale for 65 percent of the original cost. The original price of the boots is $[/tex]x, [tex]$56.12.
4. Option D: A pair of boots is on sale for 35 percent of the original cost. The original price of the boots is $[/tex]x, [tex]$56.12.
The correct scenario is:
- Option C: A pair of boots is on sale for 65 percent of the original cost. The original price of the boots is $[/tex]x, [tex]$56.12.
Option C accurately describes the situation: the original price is $[/tex]x, and after applying the 65% sale factor, the result is $3648. The equation represents this scenario correctly.
