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Difficulty: MediumBasic Algebraic Expressions and One-Step Equations

A venue manager allocates a total hospitality budget of dd dollars for an upcoming music festival. If the manager divides this budget equally among 14 performing artists, each artist receives exactly $185\$185. Which of the following equations correctly models this situation to find the total budget dd?

  1. d14=185\frac{d}{14} = 185Answer
  2. B
    14d=18514d = 185
  3. C
    d−14=185d - 14 = 185
  4. D
    d+185=14d + 185 = 14
  5. E
    185d=14\frac{185}{d} = 14

Answer

The correct equation is d14=185\frac{d}{14} = 185, which expresses that the total budget dd divided equally among 14 artists yields $185\$185 per artist.
Equal distribution of a total quantity dd across 14 recipients is mathematically represented by dividing dd by 14. Setting this quotient equal to the per-person amount of $185\$185 yields the equation d14=185\frac{d}{14} = 185.

Step-by-Step Solution

1
Identify the given quantities and variable
Total budget = dd, number of equal shares = 1414, amount per share = $185\$185
Setting up an equation requires matching the verbal scenario to mathematical operations.
2
Translate equal sharing into an algebraic operation
The total budget dd divided by 1414 is written as d14\frac{d}{14}
Dividing a total quantity into equal parts corresponds to division.
3
Equate the expression to the given share amount
d14=185\frac{d}{14} = 185
Each share is given as $185\$185.

Key Concept

Translating verbal division scenarios into one-step linear equations
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Topics

Basic Algebraic Expressions and One-Step Equations

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