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Blonde Hair Brown Eyes

Problem

In a particular class, each student has blonde hair or brown eyes; 1/4 of students with blonde hair have brown eyes and 1/3 of the students with brown eyes have blonde hair.

What fraction of the class in total have brown eyes?

Solution

This is best solved with a Venn diagram. Let the number of students with blonde hair and brown eyes be $n$. So the number of students with blonde hair will be 4$n$ (as 1/4 have both) and the number of students with brown eyes will be 3$n$ (as 1/3 have both).


From this we can determine that 3/6 = 1/2 of the class have brown eyes.

Problem ID: 145 (Jan 2004)     Difficulty: 2 Star

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