Hello, barc0de!

In carrying out a survey of the efficiency of the lights, brakes and steering of motor vehicles,

100 vehicles were found defective as follows:

35 defective lights

40 had defective brakes

41 had defective steering

8 had defective lights and brakes

7 had defective lights and steering

6 had defective brakes and steering

a) How many had defective lights, brakes and steering?

b) How many vehicles had defective lights only?

Now I know the answers are 5 and 25 respectively,

but I cannot form the correct equation to arrive at them.

I think the equation has to be in the form of:

. .

. .Right!

We are given:. .

Our equation is:

. .

. . . . .

(a) And we have: .

The best way solve part (b) is with a Venn diagram.

Or we can invent a formula for this situation . . .

We want: .

And: .

. . . . . . . . . . . . . .