The system of equations that can be used to find the price of one drink and the price of one bag of popcorn is:
9x + 2y = 28.50
5x + 10y = 42.50
The price of a bag of popcorn is $3.00
Step-by-step explanation:
Sydney and Mila go to the movie theater and purchase refreshments for their friends
- Sydney spends a total of $28.50 on 9 drinks and 2 bags of popcorn
- Mila spends a total of $42.50 on 5 drinks and 10 bags of popcorn
We need to write a system of equations that can be used to find the price of one drink and the price of one bag of popcorn and using these equations, to determine and state the price of a bag of popcorn
Assume that the price of each drink is $x and the price of each bag of popcorn is $y
∵ Sydney spends a total of $28.50 on 9 drinks and 2 bags of popcorn
∵ The price of each drink is $x
∵ The price of each bag of popcorn is $y
- Multiply 9 by x and 2 by y, add the products and equate the
sum by 28.50
∴ 9x + 2y = 28.50 ⇒ (1)
∵ Mila spends a total of $42.50 on 5 drinks and 10 bags of popcorn
∵ The price of each drink is $x
∵ The price of each bag of popcorn is $y
- Multiply 5 by x and 10 by y, add the products and equate the
sum by 42.50
∴ 5x + 10y = 42.50 ⇒ (2)
The system of equations that can be used to find the price of one drink and the price of one bag of popcorn is:
9x + 2y = 28.50
5x + 10y = 42.50
Lets solve the system of equations
∵ 9x + 2y = 28.50 ⇒ (1)
∵ 5x + 10y = 42.50 ⇒ (2)
- Multiply equation (1) by -5 to eliminate y
∵ -45x - 10y = -142.50 ⇒ (3)
Add equations (2) and (3)
∴ -40x = -100
- Divide both sides by -40
∴ x = 2.5
Substitute the value of s in equation (1) or (2) to find y
∵ 9(2.5) + 2y = 28.50
∴ 22.5 + 2y = 28.50
- Subtract both sides by 22.5
∴ 2y = 6
- Divide both sides by 2
∴ y = 3
The price of a bag of popcorn is $3.00
Learn more:
You can learn more about the system of equations in brainly.com/question/6075514
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