A survey of 121 persons was conducted at CCC, and it was found that 48 people carried a cell phone, 43 people carried a tablet computer, and 20 carried both a cell phone and a tablet.

Question

A survey of 121 persons was conducted at school, and it was found that 48 people carried a cell phone, 43 people carried a tablet computer, and 20 carried both a cell phone and a tablet.

1.  How many people carried a cell phone or a tablet?

2.  How many people carried neither a cell phone nor a tablet?

3.  How many people carried a cell phone only?

4.  How many people carried a tablet but not a cell phone?

My answers but my homework website said I was wrong....

1. 91 , 2. 10 , 3. 48 , 4. 43

Answer 1

Let C be the number of people that carried a cell phone only and T the number with tablet computer only.

Let X be the number that carried both. Let N be the number that carried neither.

So the total number of people with a cell phone is C+X, and the total of those with a tablet computer is T+X.

The total number of people is 121=C+X+T+N.

48=C+X, 43=T+X, X=20.

So C=48-20=28, T=43-20=23, N=121-28-20-23=50.

1. People carrying a cell phone or a tablet (but not both) = C+T=51. People carrying a cell phone or a tablet or both=C+T+X=71.

2. 50

3. 28

4. 23

HINT

A Venn diagram helps. In this case draw a large circle or square containing two interlocking circles. The region where the circles overlap is where the people having both devices “live” (X). The regions of the circles that don’t overlap are those with a cellphone and those with a tablet (but not both), (C and T). The region between the circles and the big circle or square is those having neither device (N). This picture helps you to put the numbers into the regions step by step so that you can actually see the whole situation.