Question

Amelia and Nora go to the movie theater and purchase refreshments for their friends. Amelia spends a total of $18.00 on 6 bags of popcorn and 3 drinks. Nora spends $31.25 on 5 bags of popcorn and 9 drinks. Write a System of equations that can be used to find the price of one bag of popcorn in the price of one drink. Using these equations determine and state the price of the drink to the nearest cent

Answer 1

Answer:

the price of the drink to the nearest cent is $2.50

Step-by-step explanation:

1 bag of popcorn = b

1 drink = d

Amelia spends this:

6b + 3d = 18.00

6b = 18 - 3d

b = 18/6 -3d/6

b = 3 - 1/2*d

Nora spends this:

5b + 9d = 31.25

9d = 31.25 - 5b

d = 31.25/9 -5/9*b

now substitute d = 31.25/9 -5/9*b in b = 3 - 1/2*d

d = 31.25/9 -5/9*(3 - 1/2*d)

d = 31.25/9 -15/9 + 5/18d

18/18d - 5/18d = 31.25/9 -15/9

13/18d = 31.25/9 -15/9

d = 18/13 * ( 31.25/9 -15/9 )

d = 2,5

The price of a drink is $2.50

EXTRA

now substitute d = 2,5 in b = 3 - 1/2*d

b = 3 - 1/2*(2.5)

b = 3 - 1.25

b = 1.75

The price of a bag of popcorn is $1.75