Question

A survey shows that 63% of the americans like cheese where 76% like apples. if x % of the americans like both cheese and apples, then :

Answer 1

answer of the ques is 39% ≤ x% ≤ 63%

Answer 2

$\huge\bf\mathfrak\green{QU}\red{ES}\blue{TION}$

A survey shows that 63% of the americans like cheese where 76% like apples. if x % of the americans like both cheese and apples

$\huge\bf\mathfrak\green{AN}\red{SW}\blue{ER}$

Let C and A denotes the percentage of people likes cheese and apples respectively.  

Given, n(C) = 63,n(A) = 76 and n(C ∩ A) = x

n(C∪A) = n(C) + n(A) − n(C ∩ A)

∴  n(C ∪ A) = 63 + 76 − x

∴  x = 139 − n(C ∪ A)

So, n(C ∪ A) ≤ 100

∴  139 − n(C ∪ A) ≥ 139 − 100 = 39

∴  x ≥ 39

Also, n(C ∩ A) ≤ n(C) and n(C ∩ A) ≤ n(A)

∴  x ≤ 63

∴ 39 ≤ x ≤ 63