A bag contains yellow, green, blue, and white marbles. The ratio of yellow, green, blue, white marbles is $4:1:2:3$. If the bag contains $20$ marbles, then how many blue marbles are there?

Answer 1

Since the ratio of yellow, green, blue, white marbles is $4:1:2:3$, we can write the number of blue marbles as $2x$ for some value of $x$. The number of blue marbles is $2x$ out of $4+1+2+3=10$ total marbles, so \[
\frac{2x}{10}=\frac{20}{100}=\frac{1}{5}.
\] Simplifying gives $2x=4$, so $x=2$. Therefore, the number of blue marbles is $2(2)=\boxed{4}$.