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Difficulty: MediumTranslating Word Phrases into Algebraic Equations

A customer's monthly utility bill is calculated as twelve dollars less than three times the sum of their base usage fee, ff, and five. If the total bill amounts to 108108, which of the following equations correctly models this calculation?

  1. 3(f+5)−12=1083(f + 5) - 12 = 108Answer
  2. B
    12−3(f+5)=10812 - 3(f + 5) = 108
  3. C
    3f+5−12=1083f + 5 - 12 = 108
  4. D
    3(5f)−12=1083(5f) - 12 = 108

Answer

The equation that correctly represents the calculation is 3(f+5)−12=1083(f + 5) - 12 = 108.
The equation is built step-by-step: 'the sum of their base usage fee, ff, and five' is written as (f+5)(f + 5). 'Three times' this sum requires multiplying the grouped expression, resulting in 3(f+5)3(f + 5). Finally, 'twelve dollars less than' means 1212 must be subtracted from that product, yielding the final correct equation 3(f+5)−12=1083(f + 5) - 12 = 108.

Step-by-Step Solution

1
Translate the phrase 'the sum of their base usage fee, ff, and five'.
(f+5)(f + 5)
The phrase 'the sum of' indicates addition between the variable ff and the number 55. Parentheses are required because a subsequent operation applies to this entire sum.
2
Translate 'three times the sum'.
3(f+5)3(f + 5)
The multiplier 33 must distribute across the entire sum, which is represented by placing it directly outside the parentheses.
3
Translate 'twelve dollars less than'.
3(f+5)−123(f + 5) - 12
The phrase 'less than' is a turnaround phrase meaning 1212 is subtracted from the quantity that precedes it conceptually, placing −12- 12 at the end.
4
Form the complete equation by setting the expression equal to the total bill.
3(f+5)−12=1083(f + 5) - 12 = 108
The phrase 'amounts to' signifies equality with the final given value of 108108.

Key Concept

Translating complex word phrases into algebraic equations requires careful attention to operation order, turnaround words like 'less than', and grouping symbols for terms like 'the sum of'.
Estimated Time:1m 0s
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Translating Word Phrases into Algebraic Equations

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