SOLUTION: there is a school play that has two prices for tickets. adults are 5$ and students are 2$. in total an amount of 900$ is collected for the play and 270 tickets are sold. how many

Question 285598: there is a school play that has two prices for tickets. adults are 5$ and students are 2$. in total an amount of 900$ is collected for the play and 270 tickets are sold. how many of each type of ticket is sold?
Answer by toidayma(44) (Show Source): You can put this solution on YOUR website!
Let x be the number of sold adult tickets, since the price of one adult ticket is $5, this number of tickets collected 5*x ($).
Let y be the number of sold student tickets, since the price of one student ticket is $2, this number of tickets collected 2*y ($).
Since the total amount of collected money is $900, we have the equation:
5*x + 2*y = 900 (1)
Since there are total 270 tickets sold., we have the equation:
x + y = 270 (2)
Now, you have to solve the system of equation (1) and (2).
From (2) we have y = 270-x (3), substitute (270-x) with y in equation (1), we get:
5*x + 2*(270-x) = 900 <-> 5*x + 540 - 2*x = 900 <-> 5*x - 2*x = 900- 540 <-> 3*x = 360 <-> x = 120. With x = 120, (3) becomes 120 + y = 270 <-> y = 150.
So, there are 120 sold adult tickets and 150 sold student tickets.
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