Question

A number of tourist were interviewed on their

choice of
means
of travell Two-thirds said
they had travel by road, 13 by air. 4
the by
both
air and road. If
20 tourist had not travel
road
Represent the information on
on a Vena
diagram:
by either
air
or road. Represent the information on a venn diagram​

Answer 1

A number of tourists were interviewed on their choice of means of travel. Two- thirds said that they travelled by road, 1330 by air and 415 by both air and road. If 20 tourists did not travel by either air or road ; (i) represent the information on a Venn diagram ; (ii) how many tourists (1) were interviewed ; (2) travelled by air only?

Answer 2

a. There were 5 tourists interviewed.

b. There was 1 tourist who traveled by air only.

Let's denote:

- R as the number of tourists traveling by road,

- A as the number of tourists traveling by air.

According to the information given:

1.
`\( (2)/(3) \)` of the tourists traveled by road,

2.
`\( (13)/(30) \)` of the tourists traveled by air,

3.
`\( (4)/(15) \)` of the tourists traveled by both air and road.

Now, let's calculate the portion of tourists who traveled only by road (\( R \) only):

`\[ \text{Portion traveling only by road} = (2)/(3) - (4)/(15) = (10)/(15) - (4)/(15) = (6)/(15) \]`

Similarly, let's calculate the portion of tourists who traveled only by air (\( A \) only):

`\[ \text{Portion traveling only by air} = (13)/(30) - (4)/(15) = (13)/(30) - (8)/(30) = (5)/(30) \]`

Now, since 20 tourists did not travel by either air or road, we can set up an equation:

`\[ \text{Portion traveling only by road} + \text{Portion traveling only by air} + \text{Portion traveling by both} + \text{Not traveling at all} = 1 \]`

`\[ (6)/(15) + (5)/(30) + (4)/(15) + \text{Not traveling at all} = 1 \]`

Solving for "Not traveling at all":

`\[ \text{Not traveling at all} = 1 - (6)/(15) - (5)/(30) - (4)/(15) \]`

`\[ \text{Not traveling at all} = (1)/(5) \]`

Now, we can find the total number of tourists interviewed (denoted as \( \alpha \)):

`\[ \alpha = \frac{1}{\text{Not traveling at all}} = (1)/((1)/(5)) = 5 \]`

So, there were 5 tourists interviewed.

Now, to find the number of tourists who traveled by air only (denoted as \( \beta \)):

`\[ \beta = \text{Portion traveling only by air} * \alpha = (5)/(30) * 5 = 1 \]`

So, there was 1 tourist who traveled by air only.

The following question may be like this:

A number of tourists were interviewed on their choice of means of travel. Two-thirds said that they travelled by road, 13/30 by air and 4/15 by both air and road. If 20 tourists did not travelled by either air or road. i. how many tourists α) were interviewed β) travelled by air only?