SOLUTION: Directions: 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

Question 92196: Directions: 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?
Answer by uma(370) (Show Source): You can put this solution on YOUR website!
Let x be the number of student tickets sold.
Let y be the number of adult tickets sold.
Then the equation is y = 2x ----------------(1)
Cost of y adult tickets at $3 each = 3y
Cost of students ticket at $2 each = 2x
Total receipt = $824
Then 2x + 3y = 824 ------------------(2)
Substituting the value for y from (1) in (2),
2x + 3(2x) = 824
==> 2x + 6x = 824
==> 8x = 824
==> x = 824/8
= 103
Thus no: of students ticket sold = 103
No: of adult tickets sold = 2*103
= 206
Good Luck!!!
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