MATH SOLVE

2 months ago

Q:
# Nora and Mackenzie go to the movie theater and purchase refreshments for their friends.Nora spends a total of $43.50 on 4 bags of popcorn and 2 drinks.Mackenzie spends a total of $17.00 on 1 bag of popcorn and 4 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 drink, to the nearest cent.

Accepted Solution

A:

The system of equations that can be used to find the price of one bagof popcorn and the price of one drink is:4 b + 2 d = 43.50b + 4 d = 17.00The price of a drink is $1.75 to the nearest centStep-by-step explanation:Nora and Mackenzie go to the movie theater and purchase refreshmentsfor their friends.Nora spends a total of $43.50 on 4 bags of popcorn and 2 drinksMackenzie spends a total of $17.00 on 1 bag of popcorn and 4 drinksLet us write the system of equations that can be used to find the priceof one bag of popcorn and the price of one drinkAssume that the price of one popcorn bag is $b and the price of onedrink is $d∵ The price of a popcorn bag = $b∵ The price of a drink = $d∵ Nora spends a total of $43.50 on 4 bags of popcorn and 2 drinks∴ 4 b + 2 d = 43.50 ⇒ (1)∵ Mackenzie spends a total of $17.00 on 1 bag of popcorn and 4 drinks∴ b + 4 d = 17.00 ⇒ (2)The system of equations that can be used to find the price of one bagof popcorn and the price of one drink is:4 b + 2 d = 43.50b + 4 d = 17.00Let us solve the system of equation to find the price of a drinkMultiply equation (2) by -4 to eliminate b∵ 4 b + 2 d = 43.50 ⇒ (1)∵ b + 4 d = 17.00 ⇒ (2)∵ (-4) b + (-4)(4) d = (-4)(17.00)∴ -4 b - 16 d = -68 ⇒ (3)- Add equations (1) and (3)∴ -14 d = -24.5- Divide both sides by -14∴ d = 1.75 ∵ d represents the price of a drink∵ d = 1.75∴ The price of a drink = $1.75The price of a drink is $1.75 to the nearest centLearn more:You can learn more about the system of equations in brainly.com/question/9045597#LearnwithBrainly