Question

Of $60$ children, $30$ are happy, $10$ are sad, and $20$ are neither happy nor sad. There are $20$ boys and $40$ girls. If there are $6$ happy boys and $4$ sad girls, how many boys are neither happy nor sad?

Answer 1

$8$ boys: Use a double-set matrix to solve this problem, with the "mood" set divided into three categories instead of only two. First, fill in the numbers given in the problem: of $60$ children, $30$ are happy, $10$ are sad, and $20$ are neither happy nor sad; $20$ are boys and $40$ are girls. You also know there are $6$ happy boys and $4$ sad girls. Therefore,by subtraction, there are $6$ sad boys and there are $8$ boys who are neither happy nor sad.

	Happy	Sad	Neither	Total
Boys	$6$	$6$	$8$	$20$
Girls		$4$		$40$
Total	$30$	$10$	$20$	$60$