Justin and lincoln go to the movie theater and purchase refreshments for their friends. justin spends a total of $14.00 on 4 drinks and 4 bags of popcorn. lincoln spends a total of $20.50 on 8 drinks and 3 bags of popcorn. write a system of equations that can be used to find the price of one drink and the price of one bag of popcorn. using these equations, determine and state the price of a bag of popcorn, to the nearest cent.

let's make p stand for popcorn and d for drinks. Using those variables, we can create our equations:

2p + 3d = 18.25

4p + 2d = 27.50

From this, we can use substitution or elimination to solve:

For substitution, in the second equations, we could factor out a 2, divide both sides by 2, and then move the left over 2p to the other side to isolate d to put into the first equation.

For elimination, we can multiply the first equation by -2 so that we can remove the 4p and focus on solving for d.

I'll be using elimination in this case:

-2(2p + 3d = 18.25) --> -4p - 6d = -36.50

-4p - 6d = -36.50

4p  + 2d = 27.50

-4d = -9.00

d = 2.25

4p + 2 * 2.25 = 27.50

4p + 4.50 = 27.50

4p = 23.00

p = 5.75

Now let's check our

2 * 5.75 + 3 * 2.25 = 18.25

11.50 + 6.75 = 18.25

18.25 = 18.25

So drinks cost $2.25 and popcorn $5.75

first option

a function is a relation in which an input is paired with exactly one output.

so, let's find the right answer.

in our first option, our inputs are january, february, and march. the outputs are 30, 28, and 25. each input has it's own output. this is correct!

our second option we know is incorrect, because ms. valverade has two outputs, dogs and cats. this is not a function.

our third option is incorrect as well. the yellow square has two ouputs, the square and the triangle.

lastly, in our fourth option, we see the number 7 two times with a different output. therefore, this is not a function.

remember: each input must be paired with only one output!