The ratio of violin players to cello players is 6 to 3. There are 8 violin players in the orchestra. How many cello players are there?

1. Problem Description

The ratio of violin players to cello players is 6 to

3. There are 8 violin players in the orchestra. How many cello players are there?

2. Solution Steps

Let $v$ be the number of violin players and $c$ be the number of cello players. We are given that the ratio of violin players to cello players is 6 to 3, which can be written as $\frac{v}{c} = \frac{6}{3}$. We are also given that there are 8 violin players, so $v = 8$.

We need to find the number of cello players, $c$. We can set up the proportion:

$\frac{8}{c} = \frac{6}{3}$

Cross-multiply to solve for $c$:

$8 \times 3 = 6 \times c$

$24 = 6c$

Divide both sides by 6:

$c = \frac{24}{6}$

$c = 4$

3. Final Answer

4