Question 41755
This is a type of mixture problem. 
The formula to remember is:
(rate of A)(amount of A) + (rate of B)(amount of B) = Total Value
.
List the known and unknown variables:
Total number of tickets:  1510
Total Value of tickets :  $6138
Total Rate A  = $5 
Amount A = "how many of each type" = x
.
Rate B = $3 
Amount of B = "how many of each type" = 1510-x because:
The Total Amount of tickets = 1510 =(Amount of A + Amount B)
So, 1510 -  A = B 
or 1510 - B = A
Depending on which part you are looking for
.
Putting it all together:
(5)(x) + (3)(1510 - x) = 6138
Simplifying:
5x + 4530 – 3x =6138
2x = 1608
2x/2= 1608/2
X = 804 or 804 adult tickets
.
1510 – 804 = 706 children tickets sold
.
Plugging x=804 back into the original equation: 
(5)(804) + (3)(1510 - 804) = 6138
4020 + 3(706) = 6138
4020 + 2118 = 6138
6138 = 6138
The answer checks out.