Question

Seventy-five cars sit on a parking lot. Thirty have stereo systems, 30 have air conditioners and 40 have sun roofs. Thirty of the cars have at least two of these three options, and 15 have all three.

Required:
a. How many cars on the lot have at least one of the three options?
b. How many have exactly one?

Answer 1

a. 55 cars

b. 25 cars

Explanation:

Let's call the number of cars with stereo systems N(ss), with air conditioners N(ac) and with sun roofs N(sr).

So we have that:

N(ss) = 30

N(ac) = 30

N(sr) = 40

N(ss and ac and sr) = 15

N(at least two) = 30

a.

To find how many cars have at least one option (N(at least one) or N(ss or ac or sr)), we have:

N(ss or ac or sr) = N(ss) + N(ac) + N(sr) - N(ss and ac) - N(ss and sr) - N(ac and sr) + N(ss and ac and sr)

N(ss or ac or sr) = 30 + 30 + 40 - (N(at least two) + 2*N(ss and ac and sr)) + 15

N(ss or ac or sr) = 30 + 30 + 40 - (30 + 2*15) + 15 = 55

b.

The number of cars that have only one option is:

N(only one) = N(at least one) - N(at least two)

N(only one) = 55 - 30 = 25