BOOKS A library contains 2000 books. There are 3 times as many non-fiction books as fiction books. Write and solve a system of equations to determine the number of non-fiction and fiction books.
let x = fiction books.
3x + x = 2000
Solve for x then 3x.
4x=2000
x=500 fiction books
y=1500 non-fiction book
Let's start by defining our variables:
Let's say that the number of fiction books is x.
The number of non-fiction books will be 3 times the number of fiction books, which can be represented as 3x.
Now we can set up our system of equations:
Equation 1: The total number of books is 2000.
x + 3x = 2000
Equation 2: The number of non-fiction books is three times the number of fiction books.
3x = x
Now, let's solve the system of equations to find the values of x and 3x:
Combining like terms in Equation 1, we have:
4x = 2000
Dividing both sides of the equation by 4:
x = 500
Now that we know the value of x, we can substitute it back into Equation 2 to find the number of non-fiction books:
3x = 3 * 500 = 1500
Therefore, there are 500 fiction books and 1500 non-fiction books in the library.
Let's define two variables to represent the number of non-fiction books and fiction books in the library.
Let's say:
x = number of non-fiction books
y = number of fiction books
From the given information, we know that the total number of books in the library is 2000:
x + y = 2000 -- Equation 1
We also know that there are 3 times as many non-fiction books as fiction books:
x = 3y -- Equation 2
Now, we have a system of equations:
x + y = 2000 -- Equation 1
x = 3y -- Equation 2
To solve this system of equations, we can use the substitution method. We can substitute the value of x from Equation 2 into Equation 1.
Substituting x = 3y into Equation 1:
3y + y = 2000
4y = 2000
y = 2000 / 4
y = 500
Now, substitute the value of y back into Equation 2 to find the value of x:
x = 3y
x = 3 * 500
x = 1500
So, there are 1500 non-fiction books and 500 fiction books in the library.