A local library has two types of books: fiction and non-fiction. The number of fiction boo… — ACT

A local library has two types of books: fiction and non-fiction. The number of fiction books is $120$ more than twice the number of non-fiction books. If the library has a total of $1\text{}860$ books, how many more fiction books than non-fiction books does the library have?

A
$580$
B
$780$
$700$ Cevap
D
$870$
E
$1\text{}280$

Cevap

The library has

700

more fiction books than non-fiction books.

The correct answer is

700

because defining the non-fiction books as

n

gives

2n + 120

fiction books. Summing these to equal

1860

yields

3n + 120 = 1860

, which solves to

n = 580

. The number of fiction books is therefore

2(580) + 120 = 1280

. The difference between the two quantities is

1280 - 580 = 700

Adım Adım Çözüm

Define variables for the two categories of books.

Let

n

be the number of non-fiction books. Then the number of fiction books,

f

, can be written as

f = 2n + 120

This translates the statement 'the number of fiction books is

120

more than twice the number of non-fiction books' into an algebraic expression.

Set up an equation representing the total number of books.

n + f = 1860 \implies n + (2n + 120) = 1860 \implies 3n + 120 = 1860

The sum of the fiction and non-fiction books must equal the total library inventory of

1860

books.

Solve the equation for the number of non-fiction books,

n

3n = 1740 \implies n = 580

Subtracting

120

from both sides and then dividing by

3

isolates the variable

n

Calculate the number of fiction books and find the difference.

Fiction books:

f = 2(580) + 120 = 1280

. Difference:

f - n = 1280 - 580 = 700

The question asks for the difference between the number of fiction and non-fiction books.

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