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Celine's Cereal Company is launching a new brand of cereal and she is considering two different sizes for the base of the boxes.



Box 1: The length is 3 times the width.

Box 2: The length is 1 less than 4 times the width.



The dimensions of the base of Box 2 are:

Awidth: $x$; length: 3
Bwidth: $x$; length: $x-4$
Cwidth: $x$; length: $4 x-1$
Dwidth: $x$; length: $4 x+1$

Verified Answer :

  • Define the width of the box as \(x\).
  • Translate the phrase "1 less than 4 times the width" into the algebraic expression \(4x - 1\).
  • Compare the derived dimensions with the provided options.
  • Identify that option c matches the calculated dimensions, so the final answer is \(\boxed{c}\).

Explanation

  1. Translating the Verbal Description to Algebraic Expressions

To identify the dimensions of the base of Box 2, we must translate the verbal description into an algebraic expression. Let the width of the base of Box 2 be represented by the variable \(x\). The problem states that the length of the base for Box 2 is "1 less than 4 times the width."

  • "4 times the width" can be written as \(4x\).
  • "1 less than" this value means we subtract 1 from it, giving us \(4x - 1\).

Therefore, the dimensions of the base of Box 2 are width \(x\) and length \(4x - 1\).

  1. Comparing with Options

We compare our derived expressions with the given options provided in the problem:

Awidth: \(x\); length: \(3\)
Bwidth: \(x\); length: \(x-4\)
Cwidth: \(x\); length: \(4x-1\)
Dwidth: \(x\); length: \(4x+1\)

Comparing our result, width \(x\) and length \(4x - 1\), with these options, it matches option c.

  1. Conclusion

The correct dimensions for the base of Box 2 correspond to option c. Thus, the width is \(x\) and the length is \(4x - 1\). The final answer is \(\boxed{c}\).

Examples

In manufacturing and design, translating specifications into mathematical formulas is a critical skill. For instance, when designing packaging, engineers use expressions like these to calculate the area of the box base, which is \(A = \text{width} \times \text{length} = x(4x - 1) = 4x^2 - x\). This formula allows the company to quickly determine material costs and optimize storage space as they change the size of the cereal boxes.

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