Final answer:
Using the ratio of 10 soccer balls to 6 volleyballs, we calculate the number of volleyballs by multiplying the volleyball ratio by 2 (since 20 soccer balls is twice the number in the ratio), resulting in 12 volleyballs.
Step-by-step explanation:
The question asks us to find the number of volleyballs in the coach's bag given the ratio of soccer balls to volleyballs and the number of soccer balls. The ratio of soccer balls to volleyballs is given as 10 to 6. If there are 20 soccer balls, we can set up a proportion to solve for the number of volleyballs in the bag.
To find the number of volleyballs, we first observe that the ratio of soccer balls to volleyballs can also be expressed as a fraction: 10/6. Since there are 20 soccer balls, which is twice the number in the ratio (10), we need to multiply the quantity of volleyballs in the ratio by the same factor of 2 to maintain the ratio.
6 (the ratio number of volleyballs) × 2 (the factor by which the number of soccer balls increased) = 12 volleyballs. Therefore, there are 12 volleyballs in the bag.