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Difficulty: MediumBasic Algebraic Expressions and One-Step Equations

A community theater group allocates a total budget of dd dollars to purchase LED stage lighting fixtures. Each fixture costs $145\$145. If the theater group purchases exactly 1212 fixtures using the total allocated budget, which of the following equations can be solved to find dd?

  1. d145=12\frac{d}{145} = 12Answer
  2. B
    145d=12145d = 12
  3. C
    145d=12\frac{145}{d} = 12
  4. D
    d−145=12d - 145 = 12
  5. E
    d+145=12d + 145 = 12

Answer

The equation representing this relationship is d145=12\frac{d}{145} = 12.
The total budget dd is divided equally among 1212 fixtures at $145\$145 each. Dividing the total budget dd by the unit price of $145\$145 equals the quantity of 1212 fixtures, which is correctly expressed as d145=12\frac{d}{145} = 12.

Step-by-Step Solution

1
Identify the relationship between total cost, unit price, and quantity.
Total Budget = (Cost per Fixture) × (Number of Fixtures)
The total money spent equals the cost per unit multiplied by the number of units purchased.
2
Substitute the given values and variable into the relationship.
d=145×12d = 145 \times 12
dd represents the total budget, $145\$145 is the cost per fixture, and 1212 is the number of fixtures.
3
Rephrase as an equivalent one-step division equation.
d145=12\frac{d}{145} = 12
Dividing both sides of d=145×12d = 145 \times 12 by 145145 isolates the quantity 1212 on one side of the equation.

Key Concept

Formulating one-step equations from real-world rate scenarios
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Topics

Basic Algebraic Expressions and One-Step Equations

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