91Ó°ÊÓ

A total of \(\$ 12,000\) is invested in two bonds that pay \(10.5 \%\) and \(12 \%\) simple interest. (There is more risk in the \(12 \%\) bond.) The combined annual interest is \(\$ 1380\). How much is invested in each bond? (a) Write a verbal model for this problem. (b) Assign labels to the verbal model. (c) Use the labels to write a linear system. (d) Solve the system and answer the question.

Ten gallons of a \(30 \%\) acid solution is obtained by mixing a \(20 \%\) acid solution with a \(50 \%\) acid solution. How many gallons of each solution must be used to obtain the desired mixture?

List the three methods for solving systems of linear equations.

In Exercises 17-22, sketch the graph of the system of linear inequalities, and label the vertices. $$ \left\\{\begin{aligned} 2 x+y & \geq 2 \\ x & \leq 2 \\ y & \leq 1 \end{aligned}\right. $$

What is a verbal model of a real-life problem?

In Exercises 29-34, use a system of linear equations to solve the problem. A van travels for 2 hours at an average speed of 40 miles per hour. How much longer must the van travel at an average speed of 55 miles per hour so that the average speed for the entire trip will be 45 miles per hour?

In Exercises 35-38, use a graphing calculator to graph the cost and revenue equations in the same viewing window. Find the sales \(x\) necessary to break even \((R=C)\) and the corresponding revenue \(R\) obtained by selling \(x\) units. (Round \(x\) to the nearest whole unit.) $$ C=0.55 x+40,000 \quad R=0.85 x $$

When should the line that corresponds to an inequality be dashed? When should it be solid?

Explain how to sketch the graph of a system of inequalities in two variables.

How do you determine the vertices of the solution region for a system of linear inequalities?