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Difficulty: MediumTranslating Word Phrases into Algebraic Equations

Match each verbal phrase or word problem to its correct algebraic equation translation.

  • Eight less than five times a number xx is equal to twenty.5x−8=205x - 8 = 20
  • A service charges 8 dollars per hour plus a 5 dollar flat fee. The total cost for xx hours is 20 dollars.8x+5=208x + 5 = 20
  • The perimeter of a rectangle is 20. Its length is 5 units more than its width, xx.2x+2(x+5)=202x + 2(x + 5) = 20
  • Five times the difference of a number xx and eight results in twenty.5(x−8)=205(x - 8) = 20

Answer

The correct matches pair each verbal description with its mathematically equivalent equation by carefully translating order of operations, rates, geometric formulas, and grouping words.
Each verbal phrase uniquely defines a single algebraic relationship. By identifying key terms such as 'less than' for reverse-order subtraction, rate contexts for variable multiplication, geometric formulas for perimeter, and grouping words for parentheses, each scenario is mapped accurately to its corresponding equation.

Step-by-Step Solution

1
Analyze the first phrase: 'Eight less than five times a number xx is equal to twenty.'
Translates to 5x−8=205x - 8 = 20.
'Five times a number' is 5x5x. The phrase 'less than' dictates that 8 is subtracted from 5x5x.
2
Analyze the second phrase: 'A service charges 8 dollars per hour plus a 5 dollar flat fee. The total cost for xx hours is 20 dollars.'
Translates to 8x+5=208x + 5 = 20.
The variable xx is multiplied by the hourly rate of 8, and the one-time flat fee of 5 is added to this product.
3
Analyze the third phrase: 'The perimeter of a rectangle is 20. Its length is 5 units more than its width, xx.'
Translates to 2x+2(x+5)=202x + 2(x + 5) = 20.
The perimeter formula is 2W+2L2W + 2L. Substituting xx for width and (x+5)(x + 5) for length provides the correct equation.
4
Analyze the fourth phrase: 'Five times the difference of a number xx and eight results in twenty.'
Translates to 5(x−8)=205(x - 8) = 20.
The word 'difference' combined with 'times' indicates that the subtraction (x−8)(x - 8) must occur first, requiring parentheses before multiplying by 5.

Key Concept

Translating complex word phrases into algebraic equations requires strict attention to operation order, grouping symbols, and contextual formulas.
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Translating Word Phrases into Algebraic Equations

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