The system of equations that can be used to find the price of one
drink and the price of one bag of popcorn is
4 x + 9 y = 43
2 x + 8 y = 25
The price of a drink is $8.50
Step-by-step explanation:
Taylor and Layla go to the movie theater and purchase refreshments
for their friends
- Taylor spends a total of $43.00 on 4 drinks and 9 bags of popcorn
- Layla spends a total of $25.00 on 2 drinks and 8 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
Assume that the price of each drink is $x and the price of each bag
of popcorn is $y
∵ Taylor spends a total of $43.00 on 4 drinks and 9 bags of popcorn
∴ 4 x + 9 y = 43 ⇒ (1)
∵ Layla spends a total of $25.00 on 2 drinks and 8 bags of popcorn
∴ 2 x + 8 y = 25 ⇒ (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
4 x + 9 y = 43
2 x + 8 y = 25
Multiply equation (2) by -2 to eliminate x
∵ -2(2 x) + -2(8 y) = -2(25)
∴ -4 x - 16 y = -50 ⇒ (3)
- Add equations (1) and (3)
∴ -7 y = -7
- Divide both sides by -7
∴ y = 1
- Substitute y in equation (1) to find x
∵ 4 x + 9(1) = 43
∴ 4 x + 9 = 43
- Subtract 9 from both sides
∴ 4 x = 34
- Divide both sides by 4
∴ x = 8.5
∵ x is the price of each drink
∴ The price of a drink = $8.50
The price of a drink is $8.50
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