Question

Find the number of students who like both peanut butter and jam. *
A group of 30 students were asked about their favourite topping for toast.
18 liked peanut butter (A)
10 liked jam (B)
6 liked neither

Answer 1

Answer:

4 students

Step-by-step explanation:

As shown in the diagram, let U=[The total number of students questioned]

$\implies n(U) = 10$

A=[Those who liked peanut butter ]

$\implies n(A) =18$

B=[Those who liked jam ]

$\implies n(B) = 10$

x = those who like both peanut butter and jam.

Also 6 liked neither peanut butter nor jam.

From the diagram we can write the mathematical equation as follow and solve for x

$30 = 18 - x + x + 10 - x + 6$

$\implies 30 = 34- x$

We add x and subtract 30 to both sides.

$\implies 30 - 30 + x = 34- x + x - 30$

$\implies x = 4$

Therefore 4 students like both peanut butter and jam.