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Difficulty: MediumTranslating Word Phrases into Algebraic Equations

Read the scenario below and fill in the missing values to complete the corresponding algebraic equation.

A network administrator calculates the total required bandwidth, BB, as seventy-five less than quadruple the sum of the base traffic, tt, and twenty.

Answer:B=B = 【4】(t+(t + 【20】)−) - 【75】

Answer

The completed equation is B=4(t+20)−75B = 4(t + 20) - 75. Therefore, blank 1 is 4, blank 2 is 20, and blank 3 is 75.
The scenario requires piecing together three mathematical operations. First, 'the sum of the base traffic, t, and twenty' creates the grouped expression (t+20)(t + 20). Next, 'quadruple' means multiplying that entire sum by 4, resulting in 4(t+20)4(t + 20). Finally, 'seventy-five less than' indicates that 75 must be subtracted from that product. Putting it all together gives 4(t+20)−754(t + 20) - 75, which fits perfectly into the provided blanks as 4, 20, and 75.

Step-by-Step Solution

1
Identify the core grouped expression.
The phrase 'the sum of the base traffic, t, and twenty' translates to (t+20)(t + 20).
The word 'sum' indicates addition, and it groups the terms together.
2
Apply the multiplication factor.
The phrase 'quadruple the sum' translates to 4(t+20)4(t + 20).
The word 'quadruple' means to multiply a quantity by 4.
3
Apply the subtraction.
The phrase 'seventy-five less than' means subtracting 75 from the entire previous expression, yielding 4(t+20)−754(t + 20) - 75.
The phrase 'less than' is a turnaround phrase, meaning the value being subtracted goes at the end of the expression.
4
Map the components to the provided equation structure.
Comparing 4(t+20)−754(t + 20) - 75 to the template B=B = blank_1 (t+(t + blank_2 )−) - blank_3, we find blank_1 is 4, blank_2 is 20, and blank_3 is 75.
This completes the algebraic translation in the required format.

Key Concept

Translating verbal descriptions of arithmetic operations and their structural order into an algebraic equation.
Estimated Time:45s
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Topics

Translating Word Phrases into Algebraic Equations

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