In a survey,74 out of 88 tourists interviewed said , that had visited at least one of the following continents : Africa, Europe, and South America .Of these , 19 had visited only Europe and Africa,30 Europe and South America, 26 South America and Africa, 10 only Europe 7 only South America and x had visited all the three continents
To find the value of x (the number of tourists who had visited all three continents), we can use the principle of inclusion-exclusion.
From the information given, we know that:
- 19 tourists had visited only Europe and Africa
- 30 tourists had visited Europe and South America
- 26 tourists had visited South America and Africa
- 10 tourists had visited only Europe
- 7 tourists had visited only South America
Let's denote the number of tourists who had visited Europe, South America, and Africa as E, S, and A respectively.
E + S + A - (19 + 30 + 26) = 74
E + S + A = 99
We also know that:
- E + (19 + 10 + x) = 88 (total number of tourists who visited Europe)
- S + (30 + 7 + x) = 88 (total number of tourists who visited South America)
- A + (26 + 19 + x) = 88 (total number of tourists who visited Africa)
E + (29 + x) = 88
S + (37 + x) = 88
A + (45 + x) = 88
Simplifying these equations, we get:
E + x = 59
S + x = 51
A + x = 43
Adding all these equations together, we have:
E + S + A + 3x = 153
Since E + S + A = 99, we can solve for x:
99 + 3x = 153
3x = 54
x = 18
Therefore, the value of x is 18. This means that 18 tourists had visited all three continents: Africa, Europe, and South America.
To find the value of x, we can use the principle of inclusion-exclusion.
Step 1: Start by adding up the number of tourists who visited only Europe, only South America, and only Africa.
- From the given data, we know that 10 tourists visited only Europe, and 7 tourists visited only South America.
So, the total number of tourists who visited only Europe or only South America is 10 + 7 = 17.
Step 2: Now, find the number of tourists who visited exactly two continents.
- We know that 19 tourists visited Europe and Africa, 30 tourists visited Europe and South America, and 26 tourists visited South America and Africa.
So, the total number of tourists who visited exactly two continents is 19 + 30 + 26 = 75.
Step 3: Subtract the number of tourists who visited exactly two continents from the total number of tourists who visited at least one of the three continents.
- As per the survey, 74 tourists visited at least one of the three continents.
So, 74 - 75 = -1.
Negative results indicate an incorrect calculation or conflicting data. In this case, the given data does not provide a consistent answer for the number of tourists who visited all three continents (continent x).