At first, there were some children and 132 adults at a party. $\frac{6}{11}$ of the adults left the party. Then another 14 children joined in the party. In the end, the number of adults who remained at the party was the same as the number of children.

1. Find the fraction of adults who remained at the party

$1 - \frac{6}{11} = \frac{5}{11}$

2. Calculate the number of adults who remained

$\frac{5}{11} \times 132 = 60$

1. Find the number of adults who remained at the party (from part a)

Number of adults at first = $132$
Fraction of adults who left = $\frac{6}{11}$
Fraction of adults who remained = $1 - \frac{6}{11} = \frac{5}{11}$
Number of adults who remained = $\frac{5}{11} \times 132 = 60$

2. Find the number of children at first

In the end, number of children = number of adults who remained = $60$
Since $14$ children joined, number of children at first = $60 - 14 = 46$

3. Find the total number of people at first

Total people at first = adults at first + children at first
Total = $132 + 46 = 178$