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Difficulty: MediumBasic Algebraic Expressions and One-Step Equations

A community library received a bulk shipment of bb new books. The head librarian distributed the entire shipment equally among 7 reading rooms, resulting in each room receiving exactly 24 books. Which of the following equations can be solved to find bb, the total number of books in the shipment?

  1. A
    7b=247b = 24
  2. B
    b−7=24b - 7 = 24
  3. b7=24\frac{b}{7} = 24Answer
  4. D
    b+7=24b + 7 = 24
  5. E
    24b=7\frac{24}{b} = 7

Answer

The equation that correctly models the situation is b7=24\frac{b}{7} = 24.
To represent distributing a total quantity bb equally into 7 parts, the total must be divided by 7. Setting this quotient equal to the per-room amount of 24 gives the one-step equation b7=24\frac{b}{7} = 24.

Step-by-Step Solution

1
Identify the total quantity and the number of equal groups.
Total quantity = bb books; Number of equal groups = 7 reading rooms.
Equal distribution of a total quantity requires dividing the total by the number of groups.
2
Set up the algebraic expression for the amount per group.
Amount per reading room = b7\frac{b}{7}.
Dividing the total number of books bb by 7 yields the share each room receives.
3
Equate the expression to the given amount per room.
b7=24\frac{b}{7} = 24.
Each room receives exactly 24 books, so the expression b7\frac{b}{7} must equal 24.

Key Concept

Translating verbal descriptions of equal sharing into one-step division equations
Estimated Time:1m 0s
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Topics

Basic Algebraic Expressions and One-Step Equations

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