Question

On a particularly boring transatlantic flight, one of the authors amused himself by counting the heads of the people in the seats in front of him. He noticed that all 28 of them either had black hair or had a whole row to themselves (or both). Of this total, 25 had black hair and 7 were fortunate enough to have a whole row of seats to themselves. How many of the black-haired people had whole rows to themselves? people

Answer 1

We shall be able to understand the problem easier on a venn diagram

People with People with People with whole row to black hair black hair themselves without row with the whole without row to 25-X themselves black hair Х (7-x) A B 28 people had either black hair, the whole row to themselves or both

Let 'x' be the number of people who had both black hair and the row to themselves

There are 25 people with black hair and 7 people with the row to themselves

will be the number of people with black hair and does not have the row to themselves

will be the number of people with the row to themselves without black hair

7 -T

As per the question, 28 people have either black hair, the whole row to themselves, or both.

That is , the sum of   will represent all the people who have either black hair, whole row to themselves, or both

We can write it in an equation as

$28=(25-x)+x+(7-x)$

28 = 32 - 1

c= 32 – 28 = 4

Hence, 4 people have the row to themselves and black hair