Let’s carefully analyze Natasha's problem and identify where she went wrong.
Natasha seems to have confused the relationship between percentages and their application to find the original value. Let’s break down the steps to find the correct attendance on Monday:
1. Understanding the Problem:
- We know that the attendance on Tuesday (300 people) is 150% of the attendance on Monday.
- We need to find out the attendance on Monday.
2. Setting Up the Equation:
- If [tex]\( x \)[/tex] represents the attendance on Monday, then 150% of [tex]\( x \)[/tex] should equal the attendance on Tuesday.
- Mathematically, this relationship can be written as:
[tex]\[
1.5x = 300
\][/tex]
3. Solving for [tex]\( x \)[/tex]:
- To solve for [tex]\( x \)[/tex], divide both sides of the equation by 1.5.
[tex]\[
x = \frac{300}{1.5}
\][/tex]
4. Calculating the Value:
-
[tex]\[
x = 200
\][/tex]
- So, the attendance on Monday was 200 people.
Natasha’s Mistake:
- Natasha incorrectly set up her proportion and made an arithmetic error in her explanation. She claimed that [tex]\(\frac{150 \times 2}{100 \times 3}=\frac{300}{?}\)[/tex].
- Instead of properly solving for [tex]\( x \)[/tex], she concluded incorrectly.
- Correct Interpretation:
- Natasha should have realized that since 300 is 150% of the attendance on Monday, you need to divide 300 by 150% (or 1.5) to find Monday's attendance.
From the given options, none exactly match the precise explanation needed to find the correct solution. However, the step where she should have divided 300 by 1.5 highlights that her understanding and subsequent operation to solve the equation were incorrect. The correct statement here as per her context, she should not have used the numbers the way she did:
- The answer is 200, indicating correctly finding that Monday had 200 people.
