Answer: 61 children attended the musical last night.
Explanation:
Let x represent the number of children that attended the musical last night.
Let y represent the number of adults that attended the musical last night.
The musical charges $3.50 for children's tickets and $5.00 for adults tickets. If the tickets sales totaled $823.50. It means that
3.5x + 5y = 823.5- - - - - - - - - - 1
Last night, twice as many adults attended the musical than children. It means that
y = 2x
Substituting y = 2x into equation 1, it becomes
3.5x + 5 × 2x = 823.5
3.5x + 10x = 823.5
13.5x = 823.5
x = 823.5/13.5
x = 61
y = 2x = 2 × 61
y = 122