SOLUTION: A survey of 830 workers in a plant indicated that 520 owned houses, 560 owned cars, 275 owned boats, 350 owned cars and houses, 220 owned houses and boats, 160 owned cars and boats
Algebra ->
Customizable Word Problem Solvers
-> Misc
-> SOLUTION: A survey of 830 workers in a plant indicated that 520 owned houses, 560 owned cars, 275 owned boats, 350 owned cars and houses, 220 owned houses and boats, 160 owned cars and boats
Log On
Question 1145089: A survey of 830 workers in a plant indicated that 520 owned houses, 560 owned cars, 275 owned boats, 350 owned cars and houses, 220 owned houses and boats, 160 owned cars and boats, and 150 owned all three.
How many of the workers did not own any of the three items?
How many of the workers owned only two of the items? Answer by ikleyn(52775) (Show Source):
(a) First calculate the number of those workers who own at least one of the items.
For it, calculate the alternate sum
560 + 560 + 275 - 350 - 220 - 160 + 150 = 815.
The rest 830 - 815 = 15 workers do not own any of the three items. ANSWER
(b) Only cars and houses 350 - 150 = 200.
Only cars and boats 160 - 150 = 10.
Only houses and boats 220 - 150 = 70.
The subsets of workers counted in the previous 3 lines are DISJOINT.
Therefore, the number of workers who own only two items is 220 + 10 + 70 = 300. ANSWER
