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Mason and his children went into a movie theater and he bought $36.50 worth of candies and pretzels. Each candy costs $4.25 and each pretzel costs $3.50. He bought 6 more pretzels than candies. Write a system of equations that could be used to determine the number of candies and the number of pretzels that Mason bought. Define the variables that you use to write the system.

Question

Mason and his children went into a movie theater and he bought 36.50worthofcandiesandpretzels.Eachcandycosts36.50 worth of candies and pretzels. Each candy costs 4.25 and each pretzel costs $3.50. He bought 6 more pretzels than candies. Write a system of equations that could be used to determine the number of candies and the number of pretzels that Mason bought. Define the variables that you use to write the system.

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Solution

Let's define the variables first:

Let C represent the number of candies Mason bought. Let P represent the number of pretzels Mason bought.

From the problem, we know two things:

  1. The total cost of candies and pretzels is 36.50.Sinceeachcandycosts36.50. Since each candy costs 4.25 and each pretzel costs $3.50, we can write this as an equation: 4.25C + 3.50P = 36.50

  2. Mason bought 6 more pretzels than candies. We can write this as an equation: P = C + 6

So, the system of equations is:

4.25C + 3.50P = 36.50 P = C + 6

This problem has been solved

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