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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

Respuesta :

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Elliot has 7 non fiction books and 19 fiction books

Let

x-------> the number of fiction books

y-------> the number of nonfiction books.

we know that

[tex] x+y=26 [/tex] -----> equation [tex] 1 [/tex]

[tex] x=y+12 [/tex]

[tex] x-y=12 [/tex] -----> equation [tex] 2 [/tex]

Add equation [tex] 1 [/tex] and equation [tex] 2 [/tex]

[tex] x+y=26\\x-y=12\\ ------\\ 2x=38\\ x=38/2\\x=19\ fiction\ books[/tex]

find the value of y

[tex] x+y=26 [/tex]

[tex] 19+y=26 [/tex]

[tex] y=26-19=7\ nonfiction\ books [/tex]

therefore

the answer is

Part a)  the number of fiction books is [tex] 19\ fiction\ books [/tex]

Part b)  the number of nonfiction books is [tex] 7\ nonfiction\ books [/tex]

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