Name: 

A rental car agency charges a flat fee of $32.00 plus $3.00 per day to rent a certain car. Another agency charges a fee of $30.50 plus $3.25 per day to rent the same car.

a.	Write a system of equations to represent the cost c for renting a car at each agency for d days.
b.	Using a graphing calculator, find the number of days for which the costs are the same. Round your answer to the nearest whole day.

An independent system of two linear equations ____ has an infinite number of solutions.

A group of 52 people attended a ball game. There were three times as many children as adults in the group. Set up a system of equations that represents the numbers of adults and children who attended the game and solve the system to find the number of children who were in the group.

The length of a rectangle is 7.8 cm more than 4 times the width. If the perimeter of the rectangle is 94.6 cm, what are its dimensions?

Equivalent systems of two linear equations ____ have the same solutions.

Your club is baking vanilla and chocolate cakes for a bake sale. They need at most 25 cakes. You cannot have more than 10 chocolate cakes. Write and graph a system of inequalities to model this system.

An exam consists of two parts, Section X and Section Y. There can be a maximum of 90 questions. There must be at least 5 more questions in Section Y than in Section X. Write a system of inequalities to model the number of questions in each of the two sections. Then solve the system by graphing.

A system of two linear inequalities ____ has a solution.

Find the values of x and y that maximize the objective function P = 3x + 2y for the graph. What is the maximum value?

Given the system of constraints, name all vertices. Then find the maximum value of the given objective function.


Maximum for

The maximum value of a linear objective function ____ occurs at exactly one vertex of the feasible region.

Your computer supply store sells two types of inkjet printers. The first, type A, costs $137 and you make a $50 profit on each one. The second, type B, costs $100 and you make a $40 profit on each one. You can order no more than 100 printers this month, and you need to make at least $4400 profit on them. If you must order at least one of each type of printer, how many of each type of printer should you order if you want to minimize your cost?

A factory can produce two products, x and y, with a profit approximated by P = 12x + 23y – 900. The production of y can exceed x by no more than 200 units. Moreover, production levels are limited by the formula What production levels yield maximum profit?

Describe the location of the point in coordinate space.
(–7, 6, –4)

Plot the point (–3, –1, 2) in a three-dimensional coordinate system.

Find the coordinates of the point in the diagram.

Which of the following points lies in the plane represented by ?

Find the equation of each trace of 6x + 4y – 12z = 36.

A food store makes a 9-lb mixture of peanuts, cashews, and raisins. Peanuts cost $1.50 per pound, cashews cost $2.00 per pound, and raisins cost $1.00 per pound. The mixture calls for twice as much peanuts than cashews. The total cost of the mixture is $13.00. How much of each ingredient did the store use?

The solution to a system of three equations in three variables is ____ one point.

Graph the system of constraints. Then find the values of x and y that maximize .

Write a second equation for the system so that the system will have no solution.
3x + 2y = –8

Graph .

Graph .

Graph .

Graph the point (–2, 0, 4).

A fish market buys tuna for $.50 per pound and spends $1.50 per pound to clean and package it. Salmon costs $2.00 per pound to buy and $2.00 per pound to clean and package. The market makes $2.50 per pound profit on tuna and $2.80 per pound profit for salmon. The market can spend only $106 per day to buy fish and $134 per day to clean it. How much of each type of fish should the market buy to maximize profit?

a.	Write an objective function P and constraints for a linear program to model the problem.
b.	Graph the constraint and find the coordinates of each vertex.
c.	Evaluate P at each vertex to find the maximum profit.

You have $50 to spend on a party. Pizzas cost $10 each, chips cost $2 per bag, and soda costs $1.25 per bottle.

a.	Write an equation in three variables for the number of pizzas, bags of chips, and bottles of soda you can buy.
b.	Find the intercepts of the equation.
c.	Graph the equation.

Tasty Bakery sells three kinds of muffins: chocolate chip muffins for $0.65 each, oatmeal muffins for $0.70 each, and blueberry muffins for $0.75 cents each. Charles buys some of each kind and chooses three more chocolate chip muffins than blueberry muffins. If he spends $6.85 on 10 muffins, how many of each type of muffin does he buy? Write and solve a system of three equations in three variables. Show your work.

Explain how to determine whether a system is independent, dependent, or inconsistent without graphing.

Explain how to solve a system of equations by substitution.