Quandaries and Queries
Who is asking: Student
Level of the question: Elementary
Question: There are 28 boys and girls in a class. Each boy collects 10 stamps and each girl collects 9 stamps. The boys have 90 stamps more than the girls. How many boy and how many girls are there?
I think this is a guess-and-check problem. There are 28 students so what happens if 14 are boys and 14 are girls.
With 14 boys and 14 girls the boys have 14 more stamps than the girls. To get 90 more we need more boys.
So what about 20 boys and 8 girls?
With 20 boys and 8 girls the boys have 128 more stamps than the girls. To get 90 more we need fewer boys.
The number of boys is between 14 and 20. Now it's your turn. Guess a number of boys between 14 and 20 and check to see how many more stamps the boys have than the girls.