Answer to Question #112671 in Algebra for Ananyae kumar bhartari

Question

40 children held hands in a large circle around the big Christmas tree.

22 of them held hands with a boy, and 30 of them held hands with a girl.

How many girls were in the circle?

Answer 1

Solution:

Note that if a child (no matter what gender) stands between two boys or between two girls, then he will once enter the account of children who hold someone's hand, and if he stands between a boy and a girl, he will be counted twice .

In this case we can determine how many children were counted twice:

22 + 30 - 40 = 12 (each of 40 was counted at least once and the fact that over 40 is counted twice).

It's mean that 12 children hold the hand of both a boy and a girl.

So, 30 - 12 = 18 - > children stand between two girls, and 12 children stand between a boy and a girl.

Let's count how many hands girls have. 18 children stand between two girls, that means they hold 36 girl’s hands, and 12 children stand between a boy and a girl, that means they hold 12 girl’s hands. In total, we get 12 + 36 = 48 girls' hands.

Answer: 48 hands correspond to 24 girls.