# A survey shows that $63\% $ of Americans like cheese whereas $76\% $ like apples. If $x\% $ of the Americans like both cheese and apples, find the value of $x$.

Answer

Verified

278.7k+ views

**Hint:**First we have to define what the terms we need to solve the problem are.

Since we need to find the value of the $x$ which is both the apples and the cheese is liked by the Americans, and now values are less liked by the Americans and mostly liked by apples. So, with this information we will find both cheese and apples lovers.

**Complete step-by-step solution:**

We need one formula to proceed which is $n(A \cup B) = n(A) + n(B) - n(A \cap B)$ which is the union of the two sets are be written as the adding of the separate plus the intersection of the negative,

Fix A is the cheese that means $n(A) = 63$ and B is the apples then $n(B) = 76$ and both the cheese and apples are liked by value of $x$ that means we have $n(A \cap B) = x$

Substitute all in the general equation we get $n(A \cup B) = 63 + 76 - x \Rightarrow 139 - x$

But since there are total only $100\% $ that means the value will not exceed hundred thus $n(A \cup B) \leqslant 100$; thus, comparing these equations we get; $139 - x \leqslant 100$$ \Rightarrow x \geqslant 39$(after cancelling)

Also, in generally we know that $n(A \cap B) \leqslant n(A)$(always less than or equals)

And hence we get $x \leqslant 63$

**Hence, we have two different values and compare them we get $39 \leqslant x \leqslant 63$ is the range of the $x$ that both apples and cheese is liked by the Americans. Minimum $39$ and maximum $63$**

**Note:**less than or equal means the values will not exceed the given points or else equals ,$n(A \cup B)$ is the totals values of the cheese lover and apples lover and also subtracts the both common lovers. $n(A \cup B) \leqslant 100$(since the most value is hundred at percent that will not exceed the hundred)

Recently Updated Pages

Which of the following would not be a valid reason class 11 biology CBSE

What is meant by monosporic development of female class 11 biology CBSE

Draw labelled diagram of the following i Gram seed class 11 biology CBSE

Explain with the suitable examples the different types class 11 biology CBSE

How is pinnately compound leaf different from palmately class 11 biology CBSE

Match the following Column I Column I A Chlamydomonas class 11 biology CBSE

Trending doubts

Which country launched the first satellite in space class 11 physics CBSE

Difference Between Plant Cell and Animal Cell

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

What is the past tense of read class 10 english CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

What is pollution? How many types of pollution? Define it

Give 10 examples for herbs , shrubs , climbers , creepers

Write a letter to the principal requesting him to grant class 10 english CBSE