Question 103089
This type of problem is generally a "mixture" problem. You need to find the "mix" of adult and child tickets that totals some dollar value, given there were n people in the audience.

Let's start by declaring x the variable for adult tickets. Since there 22 tickets sold, then there had to be 22-x child tickets.

Adult tickets sell for $13, so 13x = revenue from adult tickets

Child tickets sell for $1, so 1*(22-x) or simply 22-x = the revenue from child tickets.

The total revenue was $58, which includes adult and child ticket sales.

So, 13x + (22-x) = 58.

Removing the parenthesis and combining the x terms on the left:

12x + 22 = 58

Subtracting 22 from both sides:

12x = 36

Dividing through by 12:

x = 3

So there 3 adult tickets sold, which generates $39 revenue.

There were 22-3 = 19 child tickets sold for $1 each,  or $19 revenue.

$39 + $19 = $58. Which confirms the answer.