Final answer:
75% of the automatic transmission cars in the dealership lot have four doors. This is calculated by subtracting the percentage of manual transmission cars with four doors from the total percentage of four-door cars and then dividing by the percentage of automatic transmission cars.
Step-by-step explanation:
The question asks us to find the percentage of automatic transmission cars that have four doors at a car dealership, given certain overall percentages for transmissions and door counts as well as the combined percentage for either characteristic. Here is the step-by-step solution:
Four-door cars: 70%
Cars with either manual transmission or four doors or both: 90%
To find the percentage of automatic transmission cars with four doors, we can use a principle from set theory related to the inclusion-exclusion principle:
Percentage of automatic transmission cars with four doors = Percentage of four-door cars (-) Percentage of cars with both manual transmission and four doors
First, we can find the percentage of cars with both manual transmission and four doors:
Both manual and four doors = (Manual transmission + Four-door) (-) Either or both
60% + 70% - 90% = 40% of the cars have both a manual transmission and four doors.
Next, automatic transmission cars make up the remaining 40% of the lot (100% - 60%). To find out what percentage of these automatic transmission cars have four doors, we know that:
70% (all four-door cars) - 40% (manual and four doors) = 30% of all cars are automatic and have four doors.
Therefore, the percentage of automatic transmission cars with four doors in the lot is:
(30% / 40%) * 100 = 75%