Question

there are 50 students in a class 30 prefer tea and 35 prefer coffee how many students prefer both if each student at least one tea and coffee​

Answer 1

Answer:

The number of students who prefer both Tea and Coffee is 15.

Step-by-step explanation:

The data given in the question states that:

Total number of students in a class = 50

Number of students who prefer Tea = 30

Number of students who prefer coffee = 35

We need to find the number of students who like both coffee and tea when each student prefer at least one tea or coffee.

This means we need to find n(T∩C)

We know that,

n(T∪C) = 50

So,

n(T∪C) = n(T) + n(C) - n(T∩C)

50 = 30 + 35 - n(T∩C)

n(T∩C) = 65 - 50

n(T∩C) = 15

Answer 2

Answer:

Students prefer both if each student at least one tea and coffee​ = 15

Question : There are 50 students in a class 30 prefer tea and 35 prefer coffee how many students prefer both if each student at least one tea and coffee​

Step-by-step explanation:

From the above question,

They have given :

Total number of students in a class = 50

Number of students who prefer Tea = 30

Number of students who prefer coffee = 35

Let's assume there are x students who prefer both tea and coffee. Therefore, the remaining students must prefer either tea (30 - x) or coffee (35 - x).

30 - x + 35 - x = 50

30 + 35 - 2x = 50

65 - 2x = 50

2x = 15

x = 15/2

x = 7.5

Since there cannot be a fraction of a student, x must be rounded up to 8. Therefore, there are 8 students who prefer both tea and coffee, and 50 students in total who prefer both.

Since 30 students prefer tea and 35 students prefer coffee, there must be at least 5 students who prefer both (30 + 35 = 65; 65 - 50 = 15; 15/2 = 7.5; 7.5 rounded up = 8). Therefore, 50 students prefer both tea and coffee.

n(T∪C) = n(T) + n(C) - n(T∩C)

50 = 30 + 35 - n(T∩C)

n(T∩C) = 65 - 50

n(T∩C) = 15

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