Mathematics

Question

Elliot has a total of 26 books. He has 12 more fiction books than nonfiction books. Let x represent the number of fiction books and y represent the number of nonfiction books.
The system of equations models the total costs for each.
x + y = 26
x – y = 12
Elliot added the two equations and the result was
2x = 38.
Solve the equation. How many of each type of book does Elliot have?

fiction books

nonfiction books

2 Answer

  • Answers

    19 fiction books

    7 nonfiction books


    Explanation

    x + y = 26  ............................................. (i)

    x – y = 12  ............................................ (ii)

    Elliot added the two equations and the result was

    2x = 38.

    Dividing both sides by 2;

    x = 19

    There are 19 fiction books.

    Substituting x in equation (i),

    x + y = 26             when x = 19

    19 + y = 26

    y = 26 - 19

       = 7

    There are 7 nonfiction books

  • After solving the system of equations, Elliot has 19 fiction books and 7 nonfiction books.

    • Let x represent the number of fiction books.
    • Let y represent the number of nonfiction books.

    Given the following system of equations:

     [tex]x + y = 26\\\\x - y = 12[/tex]

    Adding the two equations together, we have:

    [tex]2x = 38[/tex]

    Dividing both sides by 2, we have:

    [tex]x = \frac{38}{2}[/tex]

    x = 19 fiction books.

    To find the value of y:

    [tex]x + y = 26\\\\y = 26 - x\\\\y = 26 - 19[/tex]

    y = 7 nonfiction books.

    Find more information: https://brainly.com/question/4728821

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