At Franklin Middle School 0.24 of the students are involved in a school sport Of these student 0.4 of them are girls Janet says this means about 0.1 of girls are involved in sports Is she correct?

Answer 1

According to the book, the answer is "yes." The book's answer is that we can determine that 0.1 of girls are involved in sports. That can't possibly be the answer because we don't know how many girls are in the class and without that missing information, the answer has to be "no." We know that 10% of all of the students are girl athletes. However, we don't know what percent of the girls are girl athletes because we don't know the breakdown of the boy to girl ratio in the class and the percentage of girl athletes as a percentage of total girls must include that information in the calculation. Here are three examples to illustrate:

Example 1

Let's assume 100 children are in the class

Let's also assume 90 boys and 10 girls make up the 100 students.

We know .24 of the students are involved in school sport.

We also know of those students who are involved in sports, 0.4 are girls.

In this example, 24 students would be involved in school sports and .4 of those 24 athletes would be girls.

In other words, 9.6 (rounded to 10) of the students are girls and 14 are boys.

In this example, all 10 girls in the class are athletes.

This is 100%, not 10% as the question asks.

Example 2

Let's assume 100 children are in the class

Let's also assume 50 boys and 50 girls make up the 100 students.

We know .24 of the students are involved in school sport.

We also know of those students who are involved in sports, 0.4 are girls.

In this example, 24 students would be involved in school sports and .4 of those 24 athletes would be girls.

In other words, 9.6 (rounded to 10) of the students are girls and 14 are boys.

In this example, 10 out of 50 girls are athletes.

This is 20%, not 10% as the question asks.

Example 3

Let's assume 100 children are in the class

Let's also assume 14 boys and 86 girls make up the 100 students.

We know .24 of the students are involved in school sport.

We also know of those students who are involved in sports, 0.4 are girls.

In this example, 24 students would be involved in school sports and .4 of those 24 athletes would be girls.

In other words, 9.6 (rounded to 10) of the students are girls and 14 are boys.

In this example, only 10 out of 86 girls are athletes.

This is 11.6%, which is close enough to 10% that the answer would be correct if that were the only possible scenario (but it isn't).