SOLUTION: You are selling tickets to your school musical. Adult tickets cost $5 and children's tickets cost $3. You sell 1510 tickets and collect $6138. Determine how many of each type of
Question 41755: You are selling tickets to your school musical. Adult tickets cost $5 and children's tickets cost $3. You sell 1510 tickets and collect $6138. Determine how many of each type of ticket were sold. Answer by tutorcecilia(2152) (Show Source):
You can put this solution on YOUR website! 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.
