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Question

Difficulty: MediumTranslating Word Phrases into Algebraic Equations

Match each verbal phrase describing a mathematical relationship or scenario to its correct algebraic expression.

  • The total cost of kk items priced at twelve dollars each, minus a five-dollar discount.12k−512k - 5
  • Twelve less than the quotient of a number kk and five.k5−12\frac{k}{5} - 12
  • The product of twelve and the quantity of five less than a number kk.12(k−5)12(k - 5)
  • The area of a rectangle with length twelve and width kk, increased by five.12k+512k + 5

Answer

The correct pairings match each contextual or mathematical description with its exact symbolic translation, respecting order of operations, geometric formulas, and grouping words.
Each correct match successfully identifies key translation words ('product', 'quotient', 'less than', 'quantity') and applies proper algebraic syntax, including necessary parentheses, geometric formulas, and the correct order for subtraction.

Step-by-Step Solution

1
Translate the rate and discount scenario.
The phrase 'kk items at twelve dollars each' translates to 12k12k. The phrase 'minus a five-dollar discount' makes it 12k−512k - 5.
Multiplication represents a per-item rate, and a discount implies subtraction.
2
Translate the quotient phrase.
The 'quotient of kk and five' is k5\frac{k}{5}. 'Twelve less than' means subtracting 1212 from this term, yielding k5−12\frac{k}{5} - 12.
The phrase 'less than' dictates reversing the order of the terms in the algebraic subtraction.
3
Translate the grouped product phrase.
The 'quantity of five less than kk' is translated as (k−5)(k - 5). The 'product of twelve and the quantity' is 12(k−5)12(k - 5).
The word 'quantity' signals that the addition or subtraction must be grouped in parentheses before applying the multiplication.
4
Translate the geometric scenario.
The 'area of a rectangle with length twelve and width kk' translates to 12k12k. 'Increased by five' adds 55, yielding 12k+512k + 5.
Area of a rectangle is calculated by multiplying length and width, and 'increased by' signifies addition.

Key Concept

Translating Word Phrases into Algebraic Equations
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Topics

Translating Word Phrases into Algebraic Equations

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