... 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.