Question

The price of admission at a movie theater is $6 for an adult and $4 for a child. In one day, the movie theater sold 80 tickets and made $420. How many adults and how many children bought tickets to the movie theater that day?
x + y = 80,
6x + 4y = 420

Which is a solution of the system of equations, and what does it represent?
(20, 60); 20 adult tickets and 60 child tickets
(30, 50); 30 adult tickets and 50 child tickets
(40, 40); 40 adult tickets and 40 child tickets
(50, 30); 50 adult tickets and 30 child tickets

Answer 1

Answer:  

Last option:  (50, 30); 50 adult tickets and 30 child tickets

Step-by-step solution:

We have the system of equations:

x+y=80

6x+4y = 420

We will use elimination method to solve it:  

Multiply the first equation by -6 and then add the equations:

- 6x - 6y = -480

 6x + 4y = 420  

We get:

-2y = -60

After dividing both sides by -2 we get:

y = 30

then plugging 30 in place of y into the original first equation we get:

x+30=80

Then subtracting 30 from both sides we get:

x = 50

The solution to the system is (50, 30)

Then notice the second equation 6x+4y=420 clear indicates that x represents the tickets for adults since the price for adults $6 is the coefficient of the x-term, while the price for children which is $4 is attached as coefficient in front of the y.

Therefore x=50 means there were sold 50 adult tickets. And y=30 that there were sold 30 child tickets.

Answer 2

x+y= 80 or x-80-y

6x+4y=420

6(80-y) + 4y = 420

480 -6y +4y=420

-2y + 480 = 420

-2y = -60

y=30

x= 80-y = 80-30=50

y=30 (Children)

x=50 ( Adults)