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Difficulty: HardTranslating Word Phrases into Algebraic Equations

Which of the following equations correctly represents the statement: 'Twelve subtracted from five times the sum of a number yy and six is equal to three less than twice the number'?

  1. 5(y+6)−12=2y−35(y + 6) - 12 = 2y - 3Answer
  2. B
    12−5(y+6)=3−2y12 - 5(y + 6) = 3 - 2y
  3. C
    5y+6−12=2y−35y + 6 - 12 = 2y - 3
  4. D
    5(y+6)−12=3−2y5(y + 6) - 12 = 3 - 2y

Answer

The equation 5(y+6)−12=2y−35(y + 6) - 12 = 2y - 3 correctly translates all verbal phrases in the appropriate order with necessary grouping symbols.
The translation process requires breaking the sentence into smaller chunks. The left side starts with 'five times the sum of a number yy and six', written as 5(y+6)5(y + 6). Then, 'twelve subtracted from' means we subtract 1212 from that product, yielding 5(y+6)−125(y + 6) - 12. The right side is 'three less than twice the number'. Twice the number is 2y2y, and three less than that is 2y−32y - 3. Setting them equal gives 5(y+6)−12=2y−35(y + 6) - 12 = 2y - 3.

Step-by-Step Solution

1
Translate 'the sum of a number yy and six'.
(y+6)(y + 6)
The word 'sum' indicates addition, and because this entire expression will be multiplied in the next step, it must be enclosed in parentheses.
2
Translate 'five times the sum'.
5(y+6)5(y + 6)
The multiplier 55 must apply to the entire grouped quantity of the sum.
3
Translate 'Twelve subtracted from' the previous result.
5(y+6)−125(y + 6) - 12
The phrase 'subtracted from' means 1212 is taken away from the established quantity, so it is placed after the minus sign.
4
Translate 'three less than twice the number'.
2y−32y - 3
First, 'twice the number' is 2y2y. 'Three less than' means 33 is subtracted from 2y2y. This forms the right side of the equation.

Key Concept

Translating complex algebraic phrases requires careful attention to grouping words like 'sum' or 'difference' and order-reversing phrases like 'less than' or 'subtracted from'.
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Topics

Translating Word Phrases into Algebraic Equations

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