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.
This system of equations models the number of books.
x + y = 26
x – y = 12
Elliot added the two equations and the result was 2x = 38.
Solve the equation. How many fiction books does Elliot have?
Answers
Answer: ["19" fiction books] ["7" nonfiction books]
Step-by-step explanation:
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Given:
Elliot has a total of 26 books. He has 12 more fiction books than nonfiction books. x represents the number of fiction books and y represent the number of nonfiction books.
x + y = 26
x – y = 12
and after adding the above two equations, Elliot get,
2x = 38
To find:
The solution to the equation and the number of fiction books that Elliot has.
Solution:
As given,
x = total number of fiction books
y = total number of non-fiction books
and,
x + y = 26 (i)
x – y = 12 (ii)
Also,
2x = 38
After solving the above, we get
x = 38/2
x = 19
which is the number of fiction books.
On putting the value of x in the equation (i), we get,
19 + y = 26
y = 26 - 19
y = 7
which is the number of non-fiction books.
Hence, the solution to the equation is x = 19 and y = 7. Also, the number of fiction books that Elliot has is 19.