At a local movie theatre, sodas cost $1..50 and bags of popcorn $4.50. Kirk goes to the movies with all of his friends. Kirk pays for all of their sodas and popcorn. It comes out to a total of $36. He pays for a total of $16 items. How many sodas, s, and how many bags of popcorn, p, does he buy?

He buys 12 sodas and 4 bags of popcorn.

Step-by-step explanation:

Here,  s represents the number of sodas and p represents the number of bags of popcorn bought.

Price of each soda = $ 1.50,

And, price of each bag of popcorn = $ 4.50,

So, the total spending = 1.50s + 4.50p   ( ∵ Total price = price of each unit × number of units )

According to the question,

1.50s + 4.50p = 36         (1)

While, total items = s + p

Again, according to the question,

s + p = 16                         (2)

Equation (1) - 1.50 × equation (2),

We get,

4.50p - 1.50p = 36 - 1.5 × 16

                  3p = 36 - 24

                  3p = 12

                   p  = 4

From equation (2),

s + 4 = 16

     s = 16 - 4

     s = 12

Hence, he buys 12 sodas and 4 bags of popcorn.