The given problem involves identifying the discrepancies in the survey results table based on the details provided:
1. Breakfast:
- Given that breakfast is preferred by one and a half times more children than adults, if the number of children preferring breakfast is 31, then the number of adults preferring breakfast would be [tex]\( \frac{31}{1.5} = \frac{31}{1.5} = 20.67 \)[/tex] (approximately 21 adults).
2. Lunch:
- There were 62 adults who responded to lunch, twice as many as the number of children. Therefore, the number of children preferring lunch would be [tex]\( \frac{62}{2} = 31 \)[/tex] children.
3. Dinner:
- Children and adults both had 24 respondents for dinner which checks out with the given data.
The results table indicates:
- Breakfast: 31 children, 45 adults (Total: 75)
- Lunch: 30 children, 62 adults (Total: 93)
- Dinner: 24 children, 48 adults (Total: 72)
- Total: 131 children, 216 adults (Total: 347)
When we verify with the results:
- Breakfast: Given 31 children and calculated 21 adults, the total should be [tex]\( 31 + 21 = 52 \)[/tex], not 75.
- Lunch: The calculated number of children is 31, but the table says 30. Therefore, this is identified as incorrect.
- Dinner: Both match the data, 24 each (total 48), checking out.
- Totals: When summing the corrected individual data:
- Correct total children: [tex]\( 31 (Breakfast) + 31 (Lunch) + 24 (Dinner) = 86 \)[/tex], but the table displays 131 which appears incorrect.
- Correct total adults: [tex]\( 21 (Breakfast) + 62 (Lunch) + 24 (Dinner) = 107 \)[/tex], but the table displays 216 which appears incorrect.
Result:
The table has errors in the "Breakfast in children" and "Lunch for children". Furthermore, the totals for Children and Adults' categories are also incorrect.
