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Difficulty: MediumTranslating Word Phrases into Algebraic Equations

The maximum payload capacity, CC, of a transport drone is equal to twice the sum of its base weight, ww, and fifty, subtracted from five hundred. Which of the following equations correctly models this capacity?

  1. C=500−2(w+50)C = 500 - 2(w + 50)Answer
  2. B
    C=2(w+50)−500C = 2(w + 50) - 500
  3. C
    C=500−2w+50C = 500 - 2w + 50
  4. D
    C=2w+50−500C = 2w + 50 - 500

Answer

The correct equation is C=500−2(w+50)C = 500 - 2(w + 50).
The correct equation translates the text sequentially while respecting mathematical grouping. First, 'the sum of its base weight, ww, and fifty' translates to the grouped expression (w+50)(w + 50). 'Twice the sum' means multiplying that entire group by 2, yielding 2(w+50)2(w + 50). Finally, 'subtracted from five hundred' dictates the order of the subtraction: 500 is the initial amount from which the expression is taken away, resulting in 500−2(w+50)500 - 2(w + 50).

Step-by-Step Solution

1
Translate the phrase 'the sum of its base weight, w, and fifty'.
(w+50)(w + 50)
The word 'sum' indicates addition, and since it is a single combined quantity, it must be enclosed in parentheses.
2
Translate the phrase 'twice the sum'.
2(w+50)2(w + 50)
The word 'twice' means multiplying by 2. It applies to the entire sum.
3
Translate the phrase 'subtracted from five hundred' to form the final equation.
C=500−2(w+50)C = 500 - 2(w + 50)
The phrase 'subtracted from X' means X is the starting amount. Therefore, the expression 2(w+50)2(w + 50) must be subtracted from 500.

Key Concept

Translating Word Phrases into Algebraic Equations
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Topics

Translating Word Phrases into Algebraic Equations

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