These three figures are called Platonic solids.

The table shows the number of vertices, edges, and faces for the tetrahedron and dodecahedron.

1. Complete the missing values for the cube. Then, make at least two observations about the number of faces, edges, and vertices in a Platonic solid.

2. There are some interesting relationships between the number of faces (), edges (), and vertices () in all Platonic solids. For example, the number of edges is always greater than the number of faces, or . Another example: The number of edges is always less than the sum of the number of faces and the number of vertices, or .

   There is a relationship that can be expressed with an equation. Can you find it? If so, write an equation to represent it.

1. Write an equation to represent each situation.  

   1. Blueberries are \$4.99 a pound. Diego buys pounds of blueberries and pays \$14.97.
   2. Blueberries are \$4.99 a pound. Jada buys pounds of blueberries and pays dollars.
   3. Blueberries are dollars a pound. Lin buys pounds of blueberries and pays dollars.
   4. Noah earned dollars over the summer. Mai earned \$275, which is \$45 more than Noah did.
   5. Noah earned dollars over the summer. Mai earned dollars, which is 45 dollars more than Noah did.
   6. Noah earned dollars over the summer. Mai earned dollars, which is dollars more than Noah did.
2. How are the equations you wrote for the blueberry purchases like the equations you wrote for Mai and Noah’s summer earnings? How are they different?

The tax on the sale of a car in Michigan is 6%. At a dealership in Ann Arbor, Michigan, a car purchase also involves \$120 in miscellaneous charges added after taxes are computed.

1. There are several quantities in this situation: the original car price, sales tax, miscellaneous charges, and total price. Write an equation to describe the relationship between all the quantities when:

   1. The original car price is \$9,500. 
   2. The original car price is \$14,699   
   3. The original price is .
2. How would the last equation you wrote change if the tax on car sales is % and the miscellaneous charges are dollars?