Answer:
Let x represents the number of children in the Broadway musical,
Since, The number of women who attended the event was 5 more than 3 times the number of children,
⇒ The number of women = 3x + 5
Also, the number of men was 3 less than 4 times the number of women,
⇒ The number of men = 4(3x+5)-3 = 12x + 20 - 3 = 12x + 17
Thus, the total number of persons = x + 3x + 5 + 12x + 17 = 16x + 22
According to the question,
16x + 22 = 2838
Which is the required equation,
Subtract 22 on both sides,
16x = 2816 ⇒ x = 176
Hence, the total number of children = 176
The number of women = 3 × 176 + 5 = 533
And, the number of men = 12 × 176 + 17 = 2129
