SOLUTION: Write a system of two equations in two unknowns for each problem. Solve each system by substitution. Tickets for a concert were sold to adults for $3 and to students for $2. I

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Write a system of two equations in two unknowns for each problem. Solve each system by substitution. Tickets for a concert were sold to adults for $3 and to students for $2. I      Log On


   

Question 104886: Write a system of two equations in two unknowns for each problem. Solve each system by substitution.
Tickets for a concert were sold to adults for $3 and to students for $2. If the total receipts were $824 and twice as many adult tickets as student tickets were sold, then how many of each were sold?
I'm struggling with how to set this problem up and solve it. Is it somthing like: 3a>2=824?
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
Revenue = Price per Unit * Number of Units Sold
R = PQ
R for adults = Ra = 3A (where A = number of adults)
R for student = Rs = 2B (where B = number of students)
Ra + Rs = 824.
Twice as many adult tickets were sold, means that A = 2B.
Substituting, we have:
Ra = 3A = 3(2B) = 6B.
Rs = 2B
Ra + Rs = 6B + 2B = 8B = 824
Dividing by 8
B = 824/8 = 103
B = number of student tickets
A = 2B = 2(103) = 206 adult tickets sold
ALWAYS check!
3(206) + 2(103) = 824
618 +206 = 824
824=824
CHECK!