Question

Luke and Aiden go to the movie theater and purchase refreshments for their friends.

Luke spends a total of $30.50 on 8 bags of popcorn and 2 drinks.

Aiden spends a total of $49.00 on 7 bags of popcorn and 6 drinks.

Write a system of equations that can be used to find the price of one bag of popcorn and the price of one drink.

Using these equations, determine and state the price of a bag of popcorn, to the nearest cent.

Answer 1

30.50 = 8p +2d

49= 7p +6d

The price of a bag of popcorn is $2.50

Explanation:

p = price of popcorn

d = price of drinks

Luke costs:

30.50 = 8p +2d

Aiden

49= 7p +6d

I will multiply Lukes equation by -3 so I can use elimination on the d variable

-3 (30.50) =-3( 8p +2d)

-91.50 = -24p -6d

Now add the modified equation to Aidens equation

49 = 7p +6d

-91.50 = -24p -6d

-------------------------

-42.5 = -17p

Divide each side by -17

-42.50/-17 = -17p/-17

2.5 = p

Each popcorn costs 2.5