# 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

Algebra ->  Algebra  -> Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> 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      Log On

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 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.