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Question

Difficulty: EasyRatio and Proportion Word Problems

A community library maintains fiction and non-fiction books in a ratio of 5:25 : 2. If the library has 350350 fiction books, how many non-fiction books are in the library?

  1. A
    100
  2. 140Answer
  3. C
    250
  4. D
    700
  5. E
    875

Answer

There are 140 non-fiction books in the library.
The ratio of fiction to non-fiction books is 5:25 : 2. Since there are 350350 fiction books, each unit of the ratio represents 3505=70\frac{350}{5} = 70 books. Multiplying the non-fiction ratio part (22) by 7070 gives 2×70=1402 \times 70 = 140 non-fiction books.

Step-by-Step Solution

1
Set up the ratio of fiction books to non-fiction books.
FictionNon-fiction=52\frac{\text{Fiction}}{\text{Non-fiction}} = \frac{5}{2}
The problem states that the ratio of fiction to non-fiction is 5 to 2.
2
Substitute the known number of fiction books (350) and let x represent the number of non-fiction books.
350x=52\frac{350}{x} = \frac{5}{2}
This establishes a direct proportion between the actual counts and the ratio values.
3
Cross-multiply and solve for x.
5x = 350 \times 2 \implies 5x = 700 \implies x = 140
Solving for x yields the total number of non-fiction books.

Key Concept

Solving ratio word problems using direct proportion
Estimated Time:45s
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Topics

Ratio and Proportion Word Problems

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