Three-fifths of the students in a room are girls. One-third of the girls have blond hair. One-half of the boys have brown hair.a. What fraction of all the students are girls with blond hair?b. What fraction of all the students are boys without brown hair?
Accepted Solution
A:
Answer: a. Of all the students, [tex]\frac{1}{5}[/tex] are girls with blond hair. b. Of all the students, [tex]\frac{1}{5}[/tex] are boys without brown hair.Step-by-step explanation:a. You know that [tex]\frac{3}{5}[/tex] of the students are girls (This means that [tex]\frac{2}{5}[/tex] of the studes are boys) and [tex]\frac{1}{3}[/tex] of these girls have blond hair. Then, [tex]\frac{1}{3}[/tex] of [tex]\frac{3}{5}[/tex] is: [tex](\frac{3}{5})(\frac{1}{3})=\frac{1}{5}[/tex] Therefore, of all the students, [tex]\frac{1}{5}[/tex] are girls with blond hair. b. You know that [tex]\frac{1}{2}[/tex] of the boys have brown hair. Then, [tex]\frac{1}{2}[/tex] of [tex]\frac{2}{5}[/tex] is: [tex](\frac{2}{5})(\frac{1}{2})=\frac{1}{5}[/tex] Of all the students, [tex]\frac{1}{5}[/tex] are boys without brown hair.