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Difficulty: MediumTranslating Word Phrases into Algebraic Equations

In a manufacturing process, the required cooling time in minutes is defined as eight subtracted from twice the sum of the baseline time, tt, and four. Which of the following algebraic expressions represents the required cooling time?

  1. 2(t+4)−82(t + 4) - 8Answer
  2. B
    8−2(t+4)8 - 2(t + 4)
  3. C
    2t+4−82t + 4 - 8
  4. D
    2(5t)−82(5t) - 8

Answer

The correct algebraic expression is 2(t+4)−82(t + 4) - 8.
The correct expression carefully follows the algebraic translation rules: 'sum' dictates the grouping (t+4)(t + 4), 'twice' multiplies that entire group by 2 to get 2(t+4)2(t + 4), and 'eight subtracted from' places the −8- 8 at the end of the expression.

Step-by-Step Solution

1
Identify and group the addition operation described in the problem.
(t+4)(t + 4)
The phrase 'the sum of the baseline time, tt, and four' indicates that these two quantities must be added and kept together as a single unit.
2
Apply the multiplication to the grouped sum.
2(t+4)2(t + 4)
The word 'twice' means multiplying the entire group by 2.
3
Translate the subtraction phrase in the correct order.
2(t+4)−82(t + 4) - 8
The phrase 'eight subtracted from' is a turnaround phrase, meaning 8 must be taken away from the grouped expression.

Key Concept

Translating complex word phrases requires identifying grouping words (like 'sum') to use parentheses, and recognizing turnaround phrases (like 'subtracted from') that reverse the written order in the mathematical expression.
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Topics

Translating Word Phrases into Algebraic Equations

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