SOLUTION: A survey of 1045 workers in a plant indicated that 660 owned houses, 800 owned cars, 355 owned boats, 500 owned cars and houses, 260 owned houses and boats, 310 owned cars and boat

Question 1133477: A survey of 1045 workers in a plant indicated that 660 owned houses, 800 owned cars, 355 owned boats, 500 owned cars and houses, 260 owned houses and boats, 310 owned cars and boats, and 250 owned all three.
(a) How many of the workers did not own any of the three items?
workers
(b) How many of the workers owned only two of the items?
workers
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.
In order to learn on how to solve such problems, look into the lessons
    - Advanced problems on counting elements in sub-sets of a given finite set
    - Challenging problems on counting elements in subsets of a given finite set
in this forum.

See also numerous solved similar problems in the archive to this forum under the links

https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1132870.html
https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1129554.html
https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1129554.html
https://www.algebra.com/algebra/homework/Rate-of-work-word-problems/Rate-of-work-word-problems.faq.question.1126097.html
https://www.algebra.com/algebra/homework/word/evaluation/Evaluation_Word_Problems.faq.question.1126099.html

From these sources, lean on how to solve such problems once and for all.

RELATED QUESTIONS
A survey of 1180 workers in a plant indicated that 620 owned houses, 680 owned cars, 445... (answered by Shin123)

A survey of 830 workers in a plant indicated that 520 owned houses, 560 owned cars, 275... (answered by ikleyn)

In survey of 900 workers 600 owned houses,500 owned cars and 345 owned boat,300 owned... (answered by math_tutor2020,ikleyn)

A survey of 51 pet owners revealed that 32 owned dogs, 38 owned cats, and 3 owned neither (answered by edjones)

A survey of 51 pet owners revealed that 32 owned dogs, 38 owned cats, and 3 owned neither (answered by sudhanshu_kmr)

From a survey of 600 college students, a marketing research company found that 400... (answered by checkley77)

A survey of 53 pet owners revealed that 25 own chickens, 21 owned pigs, 23 owned goats,... (answered by stanbon)

A survey of 51 pet owners revealed that 24 owned dogs, 28 owned cats, 11 owned turtles,... (answered by rfer)