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.
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
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