Suppose celine wants to choose a box that maximizes the amount of cereal it can hold. volume of box 1: 3x5 volume of box 2: 4x5 – x4 if celine decides the width of the cereal boxes will be greater than 1, which box will hold more cereal? explain.

The correct answer is:

Box 2

Explanation:

In these expressions, x represents the width of the box.  We are asked about widths greater than 1; let's us 1.1 as an example:

Box 1:

3(1.1⁵) = 4.83153

Box 2:

4(1.1⁵)-(1.1⁴) = 6.44204 - 1.4641 = 4.97794

With a difference as small as a tenth, the volume of box 2 is larger.  The larger the difference in width, the larger the difference in volume, and the volume of box 2 will be larger every time.

If a box has a greater volume, it can hold more cereal.

Box 2 can hold more cereal. Although the value of x is unknown, it represents a length, so it must be greater than zero. For any x > 1, the volume of Box 2 is greater than the volume of Box 1.

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