The 50 cars used by a firm were inspected. 10 had faulty brakes and 15 had faulty tyres. There were 2 cars with faulty brakes but good tyres. How many cars had good brakes and good tyres?
Using a Venn diagram, we can fill in the given information:
[asy]
label("Faulty Brakes", (0,80));
label("Faulty Tyres", (80,80));
label("Good Brakes", (40,0));
label(scale(0.8)*"$10$",(20,50));
label(scale(0.8)*"$15$",(60,50));
label(scale(0.8)*"$2$",(20,70));
filldraw(circle((30,50),20),gray(0.7));
filldraw(circle((50,50),20),gray(0.7));
[/asy]
From the diagram, we can see that there were 8 cars with only faulty brakes (i.e. not faulty tyres), and $10-2=8$ cars with both faulty brakes and faulty tyres. Therefore, we have accounted for $10+8+8+15=41$ cars. Thus, the remaining $50-41=\boxed{9}$ cars must have had good brakes and good tyres.
The answer is 33
To find out how many cars had good brakes and good tyres, we need to subtract the number of cars with faulty brakes and faulty tyres from the total number of cars.
Total number of cars = 50
Number of cars with faulty brakes = 10
Number of cars with faulty tyres = 15
Number of cars with faulty brakes and good tyres = 2
To find the number of cars with good brakes and good tyres, we can use the formula:
Number of cars with good brakes and good tyres = Total number of cars - (Number of cars with faulty brakes + Number of cars with faulty tyres - Number of cars with faulty brakes and good tyres)
Number of cars with good brakes and good tyres = 50 - (10 + 15 - 2)
Number of cars with good brakes and good tyres = 50 - 23
Number of cars with good brakes and good tyres = 27
Therefore, there were 27 cars with good brakes and good tyres.
To find out how many cars had good brakes and good tires, we need to use the concept of set theory and the given information.
Let's break down the information that we have:
- Total cars inspected = 50
- Cars with faulty brakes = 10
- Cars with faulty tires = 15
- Cars with both faulty brakes and tires = 2
To find the number of cars with good brakes and good tires, we need to subtract the number of cars with faulty brakes and faulty tires from the total number of cars inspected.
First, let's find the number of cars with faulty brakes and faulty tires:
Number of cars with faulty brakes and faulty tires = Cars with faulty brakes + Cars with faulty tires - Cars with both faulty brakes and tires
= 10 + 15 - 2
= 23
Now, we can find the number of cars with good brakes and good tires:
Number of cars with good brakes and good tires = Total cars inspected - Number of cars with faulty brakes and faulty tires
= 50 - 23
= 27
Therefore, there are 27 cars with good brakes and good tires.