Nate: \( \begin{array}{l}\text { 7. The Great Graham Cracker } \\ \text { Company places packages of their } \\ \text { graham crackers into a larger box for } \\ \text { shipping to area grocery stores. Eact } \\ \text { package of graham crackers is a righ } \\ \text { rectangular prism that measures } 18 \\ \text { cubic inches. The base of each } \\ \text { package of graham crackers } \\ \text { measures } 2 \text { inches by } 3 \text { inches. } \\ \text { Packages are placed upright into the } \\ \text { shipping box. If the larger shipping } \\ \text { box is a cube with edges that are } \\ \text { each } 30 \text { inches, how many layers of } \\ \text { graham cracker packages can the }\end{array} \) shipping box hold? Show your thinking using a visual model and equation(s).

To determine how many layers of graham cracker packages can fit inside the shipping box, we first need to calculate the dimensions of the package and the shipping box. Each package of graham crackers has a base measuring 2 inches by 3 inches and a volume of 18 cubic inches. To find the height of the package, we can use the formula for the volume of a rectangular prism, which is Volume = Base Area × Height. 1. The base area of the package is: \[ \text{Base Area} = 2 \, \text{inches} \times 3 \, \text{inches} = 6 \, \text{square inches} \] 2. Using the volume of the package: \[ 18 \, \text{cubic inches} = 6 \, \text{square inches} \times \text{Height} \] \[ \text{Height} = \frac{18 \, \text{cubic inches}}{6 \, \text{square inches}} = 3 \, \text{inches} \] Now we know each package is 3 inches tall. Next, let's calculate how many layers of packages can fit in the shipping box, which is a cube with edge lengths of 30 inches. 3. The height of the shipping box is 30 inches. To find the number of layers: \[ \text{Number of layers} = \frac{\text{Height of shipping box}}{\text{Height of one package}} = \frac{30 \, \text{inches}}{3 \, \text{inches}} = 10 \] So, the shipping box can hold **10 layers** of graham cracker packages! ### Visual Model: You can visualize this by stacking blocks. Each block represents a layer of the packages. If we have 10 layers, picture a cube that is vertically divided into 10 equal sections, and each section can hold one layer of packages. ### Final Answer: The shipping box can hold **10 layers of graham cracker packages**.