Question

There are 32 pupils in a classroom. 24 of them study one foreign language while 28 study the second foreign language. If every student studies at least one foreign language out of the two how many students study both languages. Express the number in percentages.

Answer 1

Let x represent the number of pupils that study both languages.

Let A = the set of students studiying the first language

Let B = the set of students studiying the second language

From the information given,

total number of students = 32 and they study at least one language

24 pupils study the first foreign language. This means that set A = 24

28 pupils study the second foreign language. This means that set B = 28

A diagram of the venn diagram representing this scenario is shown below

24 - x represents the pupils studying only the first language

28 - x represents the pupils studying only the second language

x represents pupils studying both languages

therefore,

24 - x + x + 28 - x = 32

- x + x - x + 24 + 28 = 32

- x + 52 = 32

x = 52 - 32

x = 20

20 pupils study both languages. We would express it as a percentage of the total number of pupils. We have

20/32 x 100

= 62.5%