It's opening day at the amusement park. There are 132 people in line before officially opens. If the ratio of adults to kids waiting to get in is 5 : 6, how many kids are waiting in line?

1 answer

To determine how many kids are waiting in line, we start by defining the ratio of adults to kids. The ratio given is \(5:6\). This means that for every 5 adults, there are 6 kids.

Let the number of adults be represented as \(5x\) and the number of kids as \(6x\) for some integer \(x\).

The total number of people in line can then be expressed as:

\[ 5x + 6x = 11x \]

According to the problem, the total number of people in line is 132. Thus, we can set up the equation:

\[ 11x = 132 \]

Next, we solve for \(x\):

\[ x = \frac{132}{11} = 12 \]

Now that we have found \(x\), we can determine the number of kids:

\[ \text{Number of kids} = 6x = 6 \times 12 = 72 \]

Therefore, the number of kids waiting in line is

\[ \boxed{72} \]