Harper went into a movie theater and bought 10 bags of popcorn and 6 drinks,

costing a total of $79. Damian went into the same movie theater and bought 3 bags of

popcorn and 5 drinks, costing a total of $36.50. Write a system of equations that

could be used to determine the price of each bag of popcorn and the price of each

drink. Define the variables that you use to write the system.

The price of a drink = $4

The price of a bag of popcorn = $5.5

Step-by-step explanation:

Let p represent popcorn and d represent drink

Harper bought 10 bags of popcorn and 6 drinks and paid $79 ➡ 10p + 6d = $79

Damian bought 3 bags of popcorn and 5 drinks and paid $36.50 ➡ 3p + 5d = $36.50

Now multiply first equation by - 3 and second equation by 10

-3 * (10p + 6d) = $79 ➡ - 30p - 18d = - $237

10 * (3p + 5d) = $36.50 ➡ 30p + 50d = $365

Now add the new equationd

30p + 50d - 30p - 18d = $365 - $237 (-30p will eliminate 30p)

32d = $128 divide both sides of the equation by 32

32 : 32d = 32 : $128 ➡ d = 4

If d = 4 that means a drink costs $4 we can use this information to find the price of a bag of popcorn

3p + 5d = $36.50 (replace d with 4)

3p + 4*5 = $36.50

3p + 20 = $36.50

3p = $36.50 - 20

3p = 16.50 divide both sides by 3

p = $5.5