Question

A bag contains yellow, green, blue, and white marbles. The ratio of yellow, green, blue, white marbles is $4:3:2:1$. If the bag contains $187$ marbles, then how many blue marbles are there?

Answer 1

Let the total number of marbles be $x$. Then, we have the following system of equations: $$\frac{4}{10}x + \frac{3}{10}x + \frac{2}{10}x + \frac{1}{10}x = x = 187.$$ Simplifying and solving for $x$, we get $x=1870$. So, there are $\frac{2}{10}\cdot 1870 = \boxed{374}$ blue marbles.