Question 1177473: II. A survey was done of 200 8-year olds asking if they like certain types of vegetables (broccoli, carrots, and green beans). The following were obtained.
28 kids only liked green beans.
73 kids liked broccoli.
40 kinds liked broccoli and green beans.
79 kids liked exactly 2 of these vegetables.
12 kinds liked broccoli and carrots, but not green beans.
34 kinds only liked carrots.
104 kids liked carrots or green beans, but not broccoli.
1. How many kids liked carrots, but not green beans?
2. How many kids liked exactly 1 of the three vegetables?
3. How many kids do not like carrots?
Found 2 solutions by CPhill, MathTherapy:
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! It's helpful to solve this kind of problem with a Venn Diagram. Here's how we can approach this:
**1. Draw a Venn Diagram**
Draw three overlapping circles representing broccoli, carrots, and green beans.
**2. Fill in the Diagram**
* **28 kids only liked green beans:** Place "28" in the green beans only section.
* **40 kids liked broccoli and green beans:** Since 73 like broccoli total, and 40 like broccoli and green beans, 73 - 40 = 33 like only broccoli and green beans. Of those, 12 also like carrots. So, place "12" in the broccoli-carrot-green bean overlap, and 33 - 12 = 21 in the broccoli-green bean overlap.
* **79 kids liked exactly 2 of these vegetables:** We've already accounted for 12 who like broccoli and carrots, and 21 who like broccoli and green beans. So, 79 - 12 - 21 = 46 must like carrots and green beans only.
* **12 kids liked broccoli and carrots, but not green beans:** Place "12" in the broccoli-carrot overlap.
* **34 kids only liked carrots:** Place "34" in the carrots only section.
* **104 kids liked carrots or green beans, but not broccoli:** This includes those who like only carrots, only green beans, and the overlap between carrots and green beans. We've already accounted for 28 + 46 = 74, so 104 - 74 = 30 must like carrots only.
**3. Calculate the Remaining Values**
* **Total who like carrots:** 30 (carrots only) + 12 (broccoli-carrot) + 46 (carrot-green bean) + 12 (all three) = 100
* **Total who like any vegetable:** Add up all the numbers in the Venn diagram.
* **Those who dislike carrots:** 200 (total) - 100 (like carrots) = 100
**Answers**
1. **How many kids liked carrots, but not green beans?** 30 (carrots only) + 12 (broccoli-carrot) = 42
2. **How many kids liked exactly 1 of the three vegetables?** 30 (carrots only) + 28 (green beans only) + 12 (broccoli and carrots only) = 70
3. **How many kids do not like carrots?** 100
Answer by MathTherapy(10551)  (Show Source):
You can put this solution on YOUR website!
II. A survey was done of 200 8-year olds asking if they like certain types of vegetables (broccoli, carrots, and green beans). The following were obtained.
28 kids only liked green beans.
73 kids liked broccoli.
40 kinds liked broccoli and green beans.
79 kids liked exactly 2 of these vegetables.
12 kinds liked broccoli and carrots, but not green beans.
34 kinds only liked carrots.
104 kids liked carrots or green beans, but not broccoli.
1. How many kids liked carrots, but not green beans?
2. How many kids liked exactly 1 of the three vegetables?
3. How many kids do not like carrots?
"RESPONDENT'S" answers are WRONG!!
Correct answers:
1. How many kids liked carrots, but not green beans? 34 + 12 = 46
2. How many kids liked exactly 1 of the three vegetables? 21 + 34 + 28 = 21 + 62 = 83
3. How many kids do not like carrots? 21 + 25 + 28 = 21 + 53 = 74
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