Jada is making lemonade for a get-together with her friends. She expects a total of 5 to 8 people to be there (including herself). She plans to prepare 2 cups of lemonade for each person.

The lemonade recipe calls for 4 scoops of lemonade powder for each quart of water. Each quart is equivalent to 4 cups.

Let represent the number of people at the get-together, the number of cups of water, the number of scoops of lemonade powder.

Select all the mathematical statements that represent the quantities and constraints in the situation.

A doctor sees between 7 and 12 patients each day. On Mondays and Tuesdays, the appointment times are 15 minutes. On Wednesdays and Thursdays, they are 30 minutes long. On Fridays, they are one hour long. The doctor works for no more than 8 hours a day.

Here are some inequalities that represent this situation.

1. What does each variable represent?
2. What does the expression in the last inequality mean in this situation?

Han wants to build a dog house. He makes a list of the materials needed:

• At least 60 square feet of plywood for the surfaces
• At least 36 feet of wood planks for the frame of the dog house 
• Between 1 and 2 quarts of paint

Han's budget is $65. Plywood costs $0.70 per square foot, planks of wood cost $0.10 per foot, and paint costs $8 per quart.

Write inequalities to represent the material constraints and cost constraints in this situation. Be sure to specify what your variables represent. 

The equation represents the volume of a cone, where is the radius of the cone and is the height of the cone.

Which equation is solved for the height of the cone?

Solve each system of equations without graphing.

There is a pair of and values that make each equation true in this system of equations:

Explain why the same pair of values also makes  true.

Which ordered pair is a solution to this system of equations? 

Which equation has exactly one solution in common with the equation ?

How many solutions does this system of equations have? Explain how you know.