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In a survey of 1,000 households — washing machines, vacuum cleaners and refrigerators were counted. Each house had at least one of these appliances. 400 had no refrigerator, 380 had no vacuum cleaner and 542 had no washing machines. 294 had both a vacuum cleaner and a washing machine, 277 had both a refrigerator and a vacuum cleaner, 120 had both refrigerator and a washing machine. How many had only a vacuum cleaner?
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In a survey of 1,000 households — washing machines, vacuum cleaners an...
Analysis of Household Appliances Survey

Given Data:
- Total number of households surveyed: 1,000
- Number of households with no refrigerator: 400
- Number of households with no vacuum cleaner: 380
- Number of households with no washing machine: 542
- Number of households with both vacuum cleaner and washing machine: 294
- Number of households with both refrigerator and vacuum cleaner: 277
- Number of households with both refrigerator and washing machine: 120

Calculating the Number of Households with Only a Vacuum Cleaner:
- Let's assume the number of households with only a refrigerator is A, only a vacuum cleaner is B, and only a washing machine is C.
- Number of households with no refrigerator = 400
- Number of households with no vacuum cleaner = 380
- Number of households with no washing machine = 542
- Number of households with both vacuum cleaner and washing machine = 294
- Number of households with both refrigerator and vacuum cleaner = 277
- Number of households with both refrigerator and washing machine = 120

Calculating the Number of Households with Only a Vacuum Cleaner:
- Total households = 1,000
- Number of households with both vacuum cleaner and washing machine = 294
- Number of households with both refrigerator and vacuum cleaner = 277
- Number of households with both refrigerator and washing machine = 120
- Number of households with all three appliances = 1,000 - (400 + 380 + 542) = 78

Calculating the Number of Households with Only a Vacuum Cleaner:
- Number of households with only a vacuum cleaner = Total households with only a vacuum cleaner - (number of households with both vacuum cleaner and washing machine + number of households with both refrigerator and vacuum cleaner + number of households with all three appliances)
- Number of households with only a vacuum cleaner = B - (294 + 277 + 78)
- Number of households with only a vacuum cleaner = B - 649

Final Calculation:
- Number of households with only a vacuum cleaner = B - 649
- Number of households with only a vacuum cleaner = Total households with only a vacuum cleaner - 649
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In a survey of 1,000 households — washing machines, vacuum cleaners and refrigerators were counted. Each house had at least one of these appliances. 400 had no refrigerator, 380 had no vacuum cleaner and 542 had no washing machines. 294 had both a vacuum cleaner and a washing machine, 277 had both a refrigerator and a vacuum cleaner, 120 had both refrigerator and a washing machine. How many had only a vacuum cleaner?
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