Respuesta :
The ratio of 5 to 6 means that for every 5 girls on the track team there are 6 boys.
So, if there are n groups of 5 girls, there should be also n groups of 6 boys. Thus, we have the proportion:
[tex]\frac{\text{ number of girls}}{\text{ number of boys}}=\frac{5}{6}[/tex]Then, let's check each item to find out which one shows possible numbers of girls to boys on the track team.
A. 24 girls, 20 boys
[tex]\frac{\text{ number of girls}}{\text{ number of boys}}=\frac{24}{20}=\frac{24\colon4}{20\colon4}=\frac{6}{5}\ne\frac{5}{6}[/tex]B. 50 girls, 56 boys
[tex]\frac{\text{ number of girls}}{\text{ number of boys}}=\frac{50}{56}=\frac{50\colon10}{56\colon10}=\frac{5}{5.6}\ne\frac{5}{6}[/tex]C. 60 girls, 50 boys
[tex]\frac{\text{ number of girls}}{\text{ number of boys}}=\frac{60}{50}=\frac{60\colon10}{50\colon10}=\frac{6}{5}\ne\frac{5}{6}[/tex]D. 20 girls, 24 boys
[tex]\frac{\text{ number of girls}}{\text{ number of boys}}=\frac{20}{24}=\frac{20\colon4}{24\colon4}=\frac{5}{6}[/tex]Therefore, option D is correct.
