Question

A florist asked a group of 75 neighbors about their flower preferences. Their responses were as tallows:34 liked daisies42 liked roses30 like daffodils16 liked both daisies and roses10 liked both daisies and daffodils20 liked both roses and daffodils7 liked all three flowers (daisies, roses, and daffodils)How many neighbors did not like any of the three flowers?

Answer 1

Given that

There are 75 neighbours.

34 liked daisies

42 liked roses

30 like daffodils

16 liked both daisies and roses

10 liked both daisies and daffodils

20 liked both roses and daffodils 7 liked all three flowers (daisies, roses, and daffodils)

Let 'x' represent the number of neighbours that did not like any of the three flowers.

Let us now represents our data in Venn diagram

The information in the venn diagram represents the following:

1) The number of neighbours that liked daisies only

= 34 - (10-7+7+16-7) = 34 - 19 = 15

2) The number of neighbours that liked roses only

= 42 - (16-7+7+20-7) = 42 - 29 = 13

3) The number of neighbours that liked daffodilis only

= 30 - (10-7+7+20-7) = 30 - 23 = 7

4) The number of neighbours that liked both daisies and roses only = 16 - 7 = 9

5) The number of neighbours that liked both daisies and daffodils only = 10 - 7 = 3

6) The number of neighbours that liked both daffodils and roses only = 20 - 7 = 13

7) The number of neighbours that liked the three flowers = 7

8) The number of neighbours that did not like the three flowers = x

Solving for x

`\begin{gathered} 15+13+7+9+3+13+7+x=75 \\ 67+x=75 \\ \end{gathered}`

Subtract 67 from both sides

`\begin{gathered} 67+x-67=75-67 \\ 67-67+x=8 \\ x=8 \end{gathered}`

Therefore, the number of neighbours that did not like any of the three flowers is 8.