Ezra and Leah took their families to the movie theater last weekend, and they each spent the same amount of money. Ezra bought 5 tickets and spent $12 on popcorn, while Leah bought 3 tickets and spent $24 on popcorn plus $9 on sodas. Which equation can you use to find p, the price of each movie ticket? Choices: (A)5 + 12p = 3 + 24p + 9p (B)5p + 12 = 3p + 24 + 9 What was the price of each movie ticket? ____ $

Question

Ezra and Leah took their families to the movie theater last weekend, and they each spent the same amount of money. Ezra bought 5 tickets and spent $12 on popcorn, while Leah bought 3 tickets and spent $24 on popcorn plus $9 on sodas. Which equation can you use to find p, the price of each movie ticket?   Choices: (A)5 + 12p = 3 + 24p + 9p (B)5p + 12 = 3p + 24 + 9  What was the price of each movie ticket?   ____ $

Bytelearn · Accepted Answer

Represent Ezra's spending: Ezra's total spending can be represented as the cost of 5 tickets plus $12 on popcorn. Leah's total spending can be represented as the cost of 3 tickets plus $24 on popcorn and $9 on sodas. Since they spent the same amount, we can set these two expressions equal to each other to find the price of each movie ticket, p.Represent Leah's spending: Write the equation representing Ezra's spending: 5p + 12 (since he bought 5 tickets and each ticket costs p dollars, plus $12 for popcorn).Set equal expressions: Write the equation representing Leah's spending: 3p + 24 + 9 (since she bought 3 tickets and each ticket costs p dollars, plus $24 for popcorn and $9 for sodas).Simplify Leah's side: Set the two expressions equal to each other because Ezra and Leah spent the same amount of money: 5p + 12 = 3p + 24 + 9.Subtract 3p: Simplify Leah's spending side of the equation by combining like terms (24 + 9): 5p + 12 = 3p + 33.Subtract 12: Subtract 3p from both sides to get the p terms on one side: 5p + 12 - 3p = 3p + 33 - 3p, which simplifies to 2p + 12 = 33.Divide by 2: Subtract 12 from both sides to solve for p: 2p + 12 - 12 = 33 - 12, which simplifies to 2p = 21.Divide both sides by 2 to find the value of p: 2p / 2 = 21 / 2, which simplifies to p = 10.5.

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