Question

(car sales) of the cars sold during the month of july, 85 had air conditioning, 98 had automatic transmission, and 78 had power steering. 6 cars had all three of these extras. 23 cars had none of these extras. 19 cars had only air conditioning, 65 cars had only automatic transmissions, and 33 cars had only power steering. 9 cars had both automatic transmission and power steering. how many cars had air conditioning and automatic transmission but not power steering? a) 6 b) 36 c) 24 d) 30 e) 3 f) none of the above.

Answer 1

To find the number of cars that had air conditioning and automatic transmission but not power steering, subtract the cars that had all three extras and the cars that had none of these extras from the number of cars that had automatic transmission and power steering.

Step-by-step explanation:

To find the number of cars that had air conditioning and automatic transmission but not power steering, we need to subtract the cars that had all three extras (6) and the cars that had none of these extras (23) from the number of cars that had automatic transmission and power steering (9). Since we know that 98 cars had automatic transmission and 78 cars had power steering, we can calculate that 98 - 9 = 89 cars had automatic transmission but not power steering. Therefore, the answer is 89 (e).

Answer 2

By using the principle of inclusion-exclusion in combinatorics and given figures, 24 cars had air conditioning and automatic transmission but not power steering.

Step-by-step explanation:

To find how many cars had air conditioning and automatic transmission but not power steering, we need to look at the provided information and use the principle of inclusion-exclusion in combinatorics.

Let's denote the following:

• Cars with air conditioning (AC): 85 cars
• Cars with automatic transmission (AT): 98 cars
• Cars with power steering (PS): 78 cars
• Cars with all three extras (AC + AT + PS): 6 cars
• Cars with none of the extras: 23 cars
• Cars with only AC: 19 cars
• Cars with only AT: 65 cars
• Cars with only PS: 33 cars
• Cars with AT and PS: 9 cars

Since there are 6 cars with all three, then the number of cars with only AT and PS can be found by subtracting the 6 from the 9 cars with both AT and PS:

AT and PS only = 9 - 6 = 3

We are looking for cars with AC and AT but not PS. We already know 6 cars have all three and 19 have only AC. Thus, the remaining number of cars must have AC and AT. We just need to exclude the cars we have already accounted for.

AC and AT only = Total AT - (AT and PS only) - (Cars with only AT) - (Cars with all three)

AC and AT only = 98 - 3 - 65 - 6 = 24

Thus, 24 cars had air conditioning and automatic transmission but not power steering.