The price of one drink is $7.5
The price of one bag of popcorn is $9.25
Step-by-step explanation:
Let us assume,
Emily spends a total of $78.50 on 2 bags of popcorn and 8 drinks.
⇒ 2x + 8y = 78.5 -------(1)
Lydia spends a total of $89.50 on 4 bags of popcorn and 7 drinks.
⇒ 4x + 7y = 89.5 --------(2)
To solve for x and y values :
Multiply eq (1) by 2 and subtract eq (2) from eq (1),
4x + 16y = 157
- (4x + 7y = 89.5)
9y = 67.5
⇒ y = 67.5/9
⇒ y = 7.5
∴ The price of one drink is $7.5
Substitute y = 7.5 in eq (1),
⇒ 2x + 8(7.5) = 78.5
⇒ 2x + 60 = 78.5
⇒ 2x = 78.5 - 60
⇒ 2x = 18.5
⇒ x = 18.5/2
⇒ x = 9.25
∴ The price of one bag of popcorn is $9.25
