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during the movie fundraising event the concession stand at the auditorium sells popcorn fruit and drinks the price of a box of popcorn is 0.50 more than

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Using the information in the exercise to develop the system of equations and using the substitution method, the following answers are found:

The system of the linear equations is P = F + 0.50, 2D = 3F - 0.50, and 2P + F + 3D = 7.75, where P = The price of a box of popcorn, D = The price of a drink, and F = The price of a piece of fruit. By other hand, the price of each item is: Popcorn = $1.50, Drink = $1.25, and Fruit = $1.

Solution of the system of equations by the Substitution Method.

Taking into account the information given in the exercise, we can write the next equations:

  1. P = F + 0.50
  2. 2D = 3F - 0.50
  3. 2P + F + 3D = 7.75

Where:

  • P = The price of a box of popcorn.
  • D = The price of a drink.
  • F = The price of a piece of fruit.

Since all equations have the variable F, we are going to use it as a key variable to represent the other variables in terms of F.

In the first equation we should not do anything, since P is in terms of F, in the second case the variable D is also in terms of F, but we need to find the value of just D, by this:

  • 2D = 3F - 0.50
  • D = (3F - 0.50) / 2
  • D = 1.5F - 0.25

We proceed to substitute the first and second equations in the third equation:

  • 2P + F + 3D = 7.75
  • 2 (F + 0.50) + F + 3 (1.5F - 0.25) = 7.75

And we solve for the variable F:

  • 2F + 1 + F + 4.5F - 0.75 = 7.75
  • 7.5F + 0.25 = 7.75
  • 7.5F = 7.75 - 0.25
  • 7.5F = 7.5
  • F = 7.5 / 7.5
  • F = 1

Now, we can solve for the variable D with the second equation:

  • 2D = 3F - 0.50
  • 2D = 3 * (1) - 0.50
  • 2D = 3 - 0.50
  • 2D = 2.5
  • D = 2.5 / 2
  • D = 1.25

Finally, we can solve for the variable P with the first equation:

  • P = F + 0.50
  • P = 1 + 0.50
  • P = 1.50

So, we have the price of each item:

  • Popcorn = 1.50
  • Drink = 1.25
  • Fruit = 1

If you want to see another exercise solved by the substitution method, you can see this link: https://brainly.com/question/22340165?referrer=searchResults

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