... sell 450 and collect 2340.how many of each type of ticket you sell?
Answers (3)
Let the number of your students be X
Let the number of your adults be Y.
Now you have X*4 dollars for the profit from students.
And you have Y*6 dollars for the profit from adults.
If you add them, which is 4X+6Y, equals to the total profit.
Likewise, if you add X and Y, which is X+Y, you can get a number of
tickets you sold.
You have to collect 2340, which is the total profit.
And you have to sell 450 tickets.
So, you can make 2 equations for this problem :
4X+6Y=2340
X+Y=450
if you solve these equations, you can get X=180, Y=270.
So, you have to sell tickets to 180 students, and 270 adults.
[solving equations]
4(X+Y)=4*450
4X+4Y=1800
subtract this equation from 4X+6Y=2340.
now you get 2Y=540.
so, Y=270, X=180
Make it like equation,
4a + 6b = 2340
a + b = 450
to get b value, multiply 2nd equation by -4
4a + 6b = 2340
-4a - 4b = -1800
----------------------
2b = 540
b = 270
We can use this b value in 1st equation to get a value,
4a + 6*270 = 2340
4a = 2340 - 1620
a = 180.
Here a is number of student tickets to sell and b is number of adults tickets to sell. Together 450 tickets.
The total cost of tickets, 4*180 + 6*270 = 720 + 1620 = 2340.