Phase 1: Owning the Dataset
Understanding the Given Information
We have a study with:
- Total participants: 3,300
- Two-thirds underestimated their meal calories
- One-quarter underestimated by at least 500 calories
Visual Representation
Let's create a number line showing participant groups:
Total Participants: 3,300
|----------------------------------------|
Underestimated (any amount): \(\frac{2}{3}\) of all
|------------------------|
Underestimated by \(\geq 500\) cal: \(\frac{1}{4}\) of all
|------|
Phase 2: Understanding the Question
We need to complete:
- Blank 1: Number of participants who underestimated (any amount)
- Blank 2: Number of participants who underestimated by at least 500 calories
The key insight: Both fractions refer to "of all participants" (the full 3,300).
Phase 3: Finding the Answer
Calculating Blank 1
Participants who underestimated = \(\frac{2}{3} \times 3,300\)
= 2,200 participants
Calculating Blank 2
Participants who underestimated by \(\geq 500\) calories = \(\frac{1}{4} \times 3,300\)
= 825 participants
Both calculations are straightforward multiplications that can be done mentally or with a calculator.
Phase 4: Solution
Final Answer:
- Statement 1: 2,200
- Statement 2: 825
These values complete the sentence: "Approximately 2,200 of the participants underestimated the calorie content of their meals, and approximately 825 of the participants underestimated the calorie content by at least 500 calories."
