Question 3402
The problem asks you to find the number of children tickets which we can call c, and the number of adult tickets, or (a).  
After establishing the variables, set up an equation to show the relationship between a and c.    C + A = 575 tickets  This first equation helps to show the relationship between the amount of tickets.  
It is also important to consider the cost of the tickets.  $4*C + $7*A = $3575
The cost of $4 per children's ticket, and &7 per adult ticket is shown through multiplication.  Each ticket is multiplied by the cost per ticket. The total being $3575 dollars in all. 

Solve the first equation for one of the variables.  
C + A = 575     C = 575 - A   The number of children's tickets is the total number of tickets 575 take away the number of adult tickets. 

Solve the second equation, by SUBSTITUTING the (C) for what it equals: 575 - A 

$4 * C     + $7*A = $3575

$4*(575-A) + $7*A = $3575

Solve by multiplying the  $4 dollars by both numbers in parentheses.  

$4*575 - $4*A  + $7*A = $3575
$2300 - $4A   +  &7A  = $3575

Next, Combine like terms  - $4A + $7A= $3A

$2300 + $3A = $3575

Solve the 2 step equation. First, subtract $2300 from both sides.  

$2300-$2300 + $3A = $3575 - $2300

$3A = $1275

Second, divide both sides by $3.

$3A     $1275
---  = ------

$3        $3

A = 425     

Now, use the A = 425 to find out what C equals.   
Go back to the first equation we wrote: C + A = 575

C + 425 = 575     Therefore C = 150, because 150+425=575

The answer then, is 425 adult tickets and 150 children's tickets

Check the answer by plugging in the number of tickets into the second equation

 $4*C  +  $7*A  = $3575
$4*150 + $7*425 = ?
$600   +  2975  = $3575