Given:
The number of students who like orange soda is n(O) = 22.
The number of students like Pepsi is n(P) = 34.
The number of students who like coke is n(C) = 20.
The number of students who like grapes is n(G) = 29.
The objective is to like the number of students like coke is 500 students are surveyed.
Explanation:
The total number of students surveyed initially is,
[tex]\begin{gathered} N=n(O)+n(P)+n(C)+n(G) \\ =22+34+20+29 \\ =105 \end{gathered}[/tex]Then, the ratio of number of students who like coke is,
[tex]\begin{gathered} r(C)=\frac{n(C)}{N} \\ r(C)=\frac{20}{105}\text{ . . . . .(1)} \end{gathered}[/tex]If 500 students are surveyed, the ratio of coke will be,
[tex]r(C)=\frac{n^{\prime}(C)}{500}\text{ . .. .. (2)}[/tex]Here, n'(C) represents the number of students who like coke when 500 students are surveyed.
To find n'(C):
On equating both equations (1) and (2),
[tex]\frac{n^{\prime}(C)}{500}=\frac{20}{105}[/tex]On further solving the above equation,
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