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?
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Solution
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.