Answer:
257
Explanation:
Let the number of Adults = x
Number of senior citizens = y
Number of children = z
x + y + z = 670 tickets
The Family Arts Center charges $22 for adults, $13 for senior citizens, and $5 for children for their live performance on Sunday afternoon.
$22 × x + $13 × y + $5 × z = $8526
22x + 13y + 5z = 8526
There were 49 more children than adults.
z = x + 49
x + y + z = 670 tickets
x + y + x + 49 = 670
2x + 49 + y = 670
y = 670 - 2x - 49
We substitute
22x + 13y + 5z = 8526
22x + 13(670 - 2x - 49) + 5(x + 49) = 8526
22x + 8710 - 26x - 637 + 5x +245 = 8526
22x + 5x - 26x + 8710 - 637 + 245 = 8526
x + 8318 = 8526
x = 8526 - 8318
x = 208
The number of Adults = 208
The number rod children is calculated as:
z = x + 49
z = 208 + 49
z = 257
The number of children = 257