1. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2010 Hawkes Learning Systems. All rights reserved. Hawkes Learning Systems: College Algebra Section 2.1b: Applications of Linear Equations in One Variable

2. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2010 Hawkes Learning Systems. All rights reserved. Objectives o Solving Formulas for one variable. o Distance and Interest problems.

3. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2010 Hawkes Learning Systems. All rights reserved. Solving Formulas for One Variable o One common task in applied mathematics is to solve a given equation in two or more variables for one of the variables. o Solving for a variable means to transform the equation into an equivalent one in which the specified variable is isolated on one side. o This is accomplished by the same methods we have already used to solve equations in Section 2.1.

4. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2010 Hawkes Learning Systems. All rights reserved. Example: Solving Formulas for One Variable Solve the following equations for the specified variable.. Solve for. Step 1: subtract 2 l from both sides of the equation. Step 2: divide by on both sides of the equation.

5. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2010 Hawkes Learning Systems. All rights reserved. Example: Solving Formulas for One Variable. Solve for.

6. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2010 Hawkes Learning Systems. All rights reserved. Example: Solving Formulas for One Variable a)v = v 0 + at ; Solve for a. b) ; Solve for F. c) A = P + Prt ; Solve for P.

7. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2010 Hawkes Learning Systems. All rights reserved. Distance and Interest Problems Good examples of linear equations arise from certain distance and simple interest problems. The basic distance formula is where is distance traveled at rate for time. The simple interest formula is where is the interest earned on principal invested at rate for time.

8. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2010 Hawkes Learning Systems. All rights reserved. Example: Interest Problems Sarah invested $8,000 in a global technology mutual fund which had an annual return rate of 14%. What amount did she earn on her investment after 1 year? Given : P = $8000 r = 14% = 0.14 and t = 1 I = (8000)(0.14)(1) I = 1120 She earned $1,120 in interest on her investment.

9. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2010 Hawkes Learning Systems. All rights reserved. Example: Other Applications a)The subtotal of items Jill bought is $18.40. If the sales tax rate is 7%, what is the total she will pay? b)Find three consecutive integers whose sum is 288. c)Find three consecutive odd integers whose sum is 165.

10. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2010 Hawkes Learning Systems. All rights reserved. Example: Distance Problems Two trucks leave a warehouse at the same time. One travels due west at an average speed of 61 miles per hour, and the other travels due east at an average speed of 53 miles per hour. After how many hours will the two trucks be 456 miles apart? Combine like terms, and solve. hours Given. Plug values in.