How many general-admission tickets were sold?

Question

Tickets to a school play cost $5.00 for general admission and $3.50 with a student ID. on opening night, 400 tickets were sold for a total of $1580. How many general-admission tickets were sold?

Answer 1

 

 

x=numbers of general admission tickets

y=numbers of tickets with student ID

 

So we have 2 equations now.

 

5x+3.5y=1580

x+y=400

 

we can make some from the 2nd equation, which is x=400-y

 

we substitute the x=400-y into the first equation

 

5(400-y)+3.5y=1580

2000-5y+3.5y=1580

2000-1.5y=1580

-1.5y=1580-2000

-1.5y=-420

y=280

 

we put y=280 into the 2nd equation

x+280=400

so x=120

 

There some other ways to solve the problem. It is my first time to answer question here, hope this can help you. 

 

Answer 2

Let x be the number of general admission tickets sold. 

Let y be the number of tickets sold with the student discount.

Total tickets sold = 400 = x + y

Total money made = 1580

Money made by selling general admission tickets = 5*x
Money made by selling discounted tickets = 3.5*y

Total money made = 5*x + 3.5*y = 1580

Now there are two equations and two variables

 

equation 1
5x + 3.5y = 1580 

 

equation 2 
x + y = 400 

Multiply equation 2 with 5 and subtract from equation 1

5x + 3.5y = 1580
- 5x - 5y = -2000
--------------------------
-1.5y = -420

y = -420/-1.5 = 280

Now, we already know that
x + y = 400

Plugging in y, we get
x + 280 = 400

x = 400-280 = 120

So x = 120 and y = 280