https://file.aiquickdraw.com/mathbot/file/1726989484561pk86s23p.jpg

Let's break down the given problem:

The question involves a survey about five popular soft drinks \( A, B, C, D, E \) in a city. It gives the following dataLet's break down the given problem:

The question involves a survey about five popular soft drinks \( A, B, C, D, E \) in a city. It gives the following 

- 96,877 persons consumed \( A \)
- 88,265 consumed \( B \)
- 1,05,227 consumed \( C \)
- 72,975 consumed \( D \)
- 59,417 consumed \( E \)
- 35,623 persons consumed \( A \) and \( B \) both
- 41,517 consumed \( B \) and \( C \) both
- 55,619 consumed \( C \) and \( D \) both
- \( A \) and \( E \) were consumed by 1,37,228 persons.

The last statement asks to find the total population of the city if the total number of persons consuming soft drinks is one-fourth of the city’s population.

### Step-by-Step Solution:

1. **Total Consumers of Soft Drinks**: 
   The total number of people who consumed soft drinks is given by adding all the individual soft drink consumers while considering overlaps (intersections). However, based on the structure of the question, the total number of unique consumers for this problem is already simplified into one-fourth of the city's population.

2. **Population Calculation**:
   The question states that one-fourth of the city’s population consumed soft drinks. Let the population of the city be \( P \), then:

   \[
   \text{Total consumers} = \frac{P}{4}
   \]

3. **Conclusion**:
   The possible answer choices provide estimates for \( P \). We need to multiply each by \( \frac{1}{4} \) to check which matches the number of consumers. Let's test this:

   - \( P = 26,283 \), then \( \frac{P}{4} = 6,570.75 \) (Not valid)
   - \( P = 16,50,256 \), then \( \frac{P}{4} = 4,12,564 \) (Not valid)
   - \( P = 22,20,584 \), then \( \frac{P}{4} = 5,55,146 \) (Not valid)
   - \( P = 33,00,532 \), then \( \frac{P}{4} = 8,25,133 \) (Not valid)

After checking the question and possible responses, the correct estimate is unclear from image details. Let me know if you would like further verification or more clarification.

**Follow-Up Questions:**
1. How does the inclusion-exclusion principle apply to surveys with overlapping categories?
2. Can we determine the number of people who consumed none of the drinks?
3. How would you adjust the analysis if some data regarding combinations of three or more drinks were given?
4. What is the significance of overlapping data in such surveys?
5. Could there be another method to estimate population size from this data?

**Tip:** Always ensure to double-check intersection data for overlapping categories in survey-based reasoning problems.

Five brands of soft drinks A, B, C, D, E are popular in a city. A survey was conducted to see the consumption of these soft drinks by persons in a day. It was found that 96,877 persons consumed A; 88,265 consumed B; 1,05,227 consumed C; 72,975 consumed D; 59,417 consumed E. It was also found that 35,623 persons consumed A and B both, 41,517 consumed B and C both, 55,619 consumed C and D both, whereas A and E both were consumed by 1,37,228 persons. If the total number of persons consuming soft drinks in a day forms one-fourth of the population of the city, then the population of the city is:

This problem involves a survey on the consumption of five soft drinks in a city. Learn how to apply set theory and the inclusion-exclusion principle to calculate the total population based on consumption data. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation