Respuesta :
So we are told that each marble bag has 5 orange marbles for every 6 purple ones. Then the proportion of orange marbles is:
[tex]\frac{5}{6}[/tex]This proportion has to be the same for any amount of marbles in a bag. If we use x for the number of purple marbles we are looking for we have that the proportion of orange marbles in a bag with 30 orange marbles is given by:
[tex]\frac{30}{x}[/tex]As I stated before, this proportion has always the same value so we can equalize both expressions:
[tex]\frac{5}{6}=\frac{30}{x}[/tex]We need to solve this for x. We can multiply x to both sides of the equation:
[tex]\begin{gathered} \frac{5}{6}\cdot x=\frac{30}{x}\cdot x \\ \frac{5}{6}x=30 \end{gathered}[/tex]Then we multiply both sides by 6/5:
[tex]\begin{gathered} \frac{6}{5}\cdot\frac{5}{6}x=\frac{6}{5}\cdot30 \\ x=36 \end{gathered}[/tex]Then the answer is that the bag contains 36 purple marbles.
