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Difficulty: MediumTranslating Word Phrases into Algebraic Equations

A structural engineer calculates the maximum safe load, LL, for a support beam. The safe load is equal to fifty less than triple the sum of the beam's cross-sectional area, AA, and twelve. What algebraic equation models the maximum safe load?

  1. L=3(A+12)−50L = 3(A + 12) - 50Answer
  2. B
    L=50−3(A+12)L = 50 - 3(A + 12)
  3. C
    L=3A+12−50L = 3A + 12 - 50
  4. D
    L=3(A+12)+50L = 3(A + 12) + 50

Answer

The correct equation is L=3(A+12)−50L = 3(A + 12) - 50.
The correct equation methodically translates the text: 'the sum of... A, and twelve' becomes the grouped quantity (A + 12). 'Triple' multiplies this entire group by 3, giving 3(A + 12). Finally, 'fifty less than' dictates subtracting 50 from that product, yielding 3(A + 12) - 50.

Step-by-Step Solution

1
Identify the base quantity being modified.
The phrase 'the sum of the beam's cross-sectional area, AA, and twelve' translates algebraically to the grouped expression (A+12)(A + 12).
The word 'sum' implies addition, and it creates a single quantity that must be grouped in parentheses before further operations are applied.
2
Translate the multiplier.
The word 'triple' indicates multiplication by 3, resulting in the expression 3(A+12)3(A + 12).
The multiplier applies to the entire sum identified in the previous step.
3
Translate the subtraction phrase.
The phrase 'fifty less than' means subtracting 50 from the previously established quantity, yielding 3(A+12)−503(A + 12) - 50.
In algebraic translation, 'X less than Y' dictates an order reversal to become Y - X.
4
Form the final equation.
Set the maximum safe load, LL, equal to the derived expression: L=3(A+12)−50L = 3(A + 12) - 50.
The problem states that the safe load is equal to the verbal expression.

Key Concept

Translating order-dependent phrases and implied grouping symbols from English into algebraic notation.
Estimated Time:45s
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Topics

Translating Word Phrases into Algebraic Equations

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