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Difficulty: MediumTranslating Word Phrases into Algebraic Equations

An aircraft's current cruising altitude is aa feet. The required altitude for a new training maneuver is defined as four hundred feet less than triple the sum of the current altitude and two thousand. Which of the following algebraic expressions represents the required altitude in feet?

  1. 3(a+2000)−4003(a + 2000) - 400Answer
  2. B
    400−3(a+2000)400 - 3(a + 2000)
  3. C
    3a+2000−4003a + 2000 - 400
  4. D
    3(2000a)−4003(2000a) - 400

Answer

The correct expression is 3(a+2000)−4003(a + 2000) - 400.
The correct answer accurately models the sequence of operations described in the text. It uses parentheses to group the addition (a+2000)(a + 2000), multiplies that entire group by 3, and places the subtraction of 400 at the end of the expression to correctly satisfy the 'less than' condition.

Step-by-Step Solution

1
Translate 'the sum of the current altitude and two thousand'.
(a+2000)(a + 2000)
The word 'sum' indicates addition between the variable aa and the number 2000. Parentheses are required because subsequent operations apply to this entire result.
2
Apply the multiplier 'triple' to the sum.
3(a+2000)3(a + 2000)
'Triple' means multiplying the entire grouped quantity by 3.
3
Incorporate the phrase 'four hundred feet less than'.
3(a+2000)−4003(a + 2000) - 400
The phrase 'less than' is a turnaround phrase, meaning the 400 must be subtracted from the previously established quantity.

Key Concept

Translating multi-step verbal phrases into algebraic expressions requires careful attention to grouping symbols and translation order, particularly for subtraction.
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Translating Word Phrases into Algebraic Equations

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