Emily and sophia go to the movie theater and purchase refreshments for their friends.

emily spends a total of $45.50 on 7 drinks and 4 bags of popcorn.

sophia spends a total of $25.50 on 4 drinks and 2 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.

7 d + 4 p = 45.50

4d + 2p = 25.50

bag of popcorn = $1.75

Step-by-step explanation:

Emily's equation:

Sophia's equation

Where:

d = price of a drink

p = price of a bag of popcorn

Solving for p in Sophia's equation

4p =45.50 - 7d

p = (45.50 -7d)/4

p = 11.375 -1.75 d

Replacing the value of "p" in Emily's equation:

4d + 2p = 25.50

4d + 2 (11.375 -1.75 d) =25.50

4d +22.75 -3.5d =25.50

4d-3.5d =25.50-22.75

0.5 d= 2.75

d= 2.75/0.5

d = 5.5 (price of each drink)

Finally, replacing the value of "d" in Emily's equation:

7(5.5) + 4 p =45.5

38.5 +4p =45.5

4p =45.5-38.5

4p =7

p =7/4= $1.75