Alexander and Matthew go to the movie theater and purchase refreshments for their friends. Alexander spends a total of $60.00 on 2 drinks and 9 bags of popcorn. Matthew spends a total of $60.00 on 10 drinks and 5 bags of popcorn. Write a system of equations that can be used to find the price of one drink and the price of one bag of popcorn. Using these equations, determine and state the price of a bag of popcorn, to the nearest cent.

Question

Cameron Ramsey

Mathematics

10 September, 06:40

Alexander and Matthew go to the movie theater and purchase refreshments for their friends. Alexander spends a total of $60.00 on 2 drinks and 9 bags of popcorn. Matthew spends a total of $60.00 on 10 drinks and 5 bags of popcorn. Write a system of equations that can be used to find the price of one drink and the price of one bag of popcorn. Using these equations, determine and state the price of a bag of popcorn, to the nearest cent.

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Answers (1)

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Dario Weiss · Answer 1

2x + 9y = 60

10x + 5y = 60

The price of each bag of popcorn is $6.

Step-by-step explanation:

Let each drink costs $x and the price of each bag of popcorn is $y.

So, from the given two conditions we can write two different equations as

2x + 9y = 60 ... (1) and

10x + 5y = 60 ... (2)

Now, solving those two equations we get,

5 (60 - 9y) + 5y = 60

⇒ 300 - 45y + 5y = 60

⇒ 40y = 240

⇒ y = 6

Therefore, the price of each bag of popcorn is $6. (Answer)