Suppose Celine wants to choose a box that maximizes the amount of cereal it can hold.Volume of Box 1: 3x5Volume of Box 2: 4x5 – x4If Celine decides the width of the cereal boxes will be greater than 1, which box will hold more cereal? Explain.

Answer:

Box 2 will hold more cereal. To compare the two volumes, subtract the volume of Box 1 from the volume of Box 2: $(4x^5 - x^4) - (3x^5) = x^5 - x^4$. Since Celine decided that the width, $x$, will be greater than 1, $x^5$ will always be greater than $x^4$. This makes the difference $(x^5 - x^4)$ a positive value, meaning Box 2's volume is greater than Box 1's volume for all $x > 1$.