Lincoln went into a movie theater and bought 2 bags of popcorn and 4 candies, costing a total of \( \$ 34 \). Zoey went into the same movie theater and bought 6 bags of popcorn and 5 candies, costing a total of \( \$ 74 \). Determine the price of each bag of popcorn and the price of each candy. Answer Attempt 1 out of 10 Each bag of popcorn costs \( \$ \square \) and each candy costs \( \$ \square \).

Let's denote the price of each bag of popcorn as \( p \) and the price of each candy as \( c \). We can set up the following equations based on the information given: 1) \( 2p + 4c = 34 \) (from Lincoln's purchase) 2) \( 6p + 5c = 74 \) (from Zoey's purchase) To solve these equations, we can first simplify the first equation: Divide the first equation by 2: \( p + 2c = 17 \) (Equation 1) Now we substitute \( p \) from Equation 1 into the second equation: From Equation 1, we rearrange it to find \( p \): \( p = 17 - 2c \) Now, substitute \( p \) into the second equation: \( 6(17 - 2c) + 5c = 74 \) \( 102 - 12c + 5c = 74 \) Combine like terms: \( 102 - 7c = 74 \) Now, isolate \( c \): \( 102 - 74 = 7c \) \( 28 = 7c \) \( c = 4 \) Now that we have \( c \), substitute it back to find \( p \): \( p + 2(4) = 17 \) \( p + 8 = 17 \) \( p = 17 - 8 \) \( p = 9 \) Therefore, each bag of popcorn costs \( \$ 9 \) and each candy costs \( \$ 4 \). Each bag of popcorn costs \( \$ 9 \) and each candy costs \( \$ 4 \).