Chapter 2 Sections 5 & 6: Problem Solving

1. Chapter 2 Sections 5 & 6: Problem Solving • In this section, we will… • Solve general word problems and applications • Use formulas to solve word problems

2. How to Solve a Word Problem: • Step 1: Read the problem until you understand it. • What are we asked to find? • What information is given? • What vocabulary is being used? • Step 2: Assign a variable to represent what you are looking for. • Express any remaining unknown quantities in terms of this variable. • Step 3: Make a list of all known facts and form an equation or inequality to solve. • It may help to make a labeled: diagram, table or chart, graph • Step 4: Solve • Step 5: State the solution in a complete sentence by mirroring the original question. • Be sure to include units when necessary. • Step 6: Check your result(s) in the words of the problem • Does your solution make sense? 2.5 Solve Word Problems and Applications

3. Example:To cut down on vandalism, a lot on which a house is to be constructed was completely fenced. The north side of the lot was 205 feet in length. The west and east sides were 275 and 210 feet respectively in length. If 945 feet of fencing was used, how long is the south side of the lot? 2.5 Solve Word Problems and Applications

4. Example:Torrential rains caused the width of a river to swell to 84 feet. If this was twice its normal size, how wide was the river before the flooding? Example: An engine repair costs a truck owner $690 in parts plus $45 per hour to pay for labor. If the repair totaled $1,185, how many hours did the repair take? 2.5 Solve Word Problems and Applications

5. Example:Over a four-year span, improvements to a Hollywood movie studio tour caused it to take longer. The first year, 10 minutes were added to the tour length. In the second, third and fourth years, 5 minutes were added each year. If the tour now lasts 135 minutes, how long was the tour originally? 2.5 Solve Word Problems and Applications

6. Example:What is the measure of the angle between each of the “spokes” of the Ferris wheel shown below? ? 2.5 Solve Word Problems and Applications

7. Example:A plumber wants to cut a 17-foot pipe into three sections. The longest section is to be three times as long as the shortest, and the middle-sized section is to be 2 feet longer than the shortest. How long is each section of pipe to be? Example:Two septic tanks hold a total of 45 gallons of a toxic solvent. One tank holds 6 gallons more than twice the amount in the other. How many gallons does each tank hold? 2.6 Solve General Word Problems and Applications

8. Example:What is the sum of the measures of the angles of any triangle? Example:For a bicycle frame, the angle that the horizontal crossbar makes with the seat support is 15 degrees less than twice the angle at the steering column. The angle at the pedal gear is 25 degrees more than the angle of the steering column. Find these three angle measures. 2.6 Solve General Word Problems and Applications

9. We will use the following formulas from section 2.5: • read the problem and select the appropriate formula • construct a table with the formula as a heading • use the information in the problem and the formula • to complete the table • solve the equation that emerges from the table • answer the question and check simple interest formula Don’t forget to change your percent to a decimal before using it in a formula! 2.6 Use Formulas to Solve Word Problems

10. Example:When a husband and wife leave for work, they drive in opposite directions. Their average speeds are different; however, their drives last the same amount of time. Complete the table below. • Example:Complete the table and answer the questions below. • What type of brush does the store have the largest quantity of? • What is the total value of the inventory of brushes? 2.6 Use Formulas to Solve Word Problems

11. Example:Complete the table below and answer the questions below. • How much more money is invested in the brother in law’s business than the certificate of deposit? • What is the total amount of interest the couple will make from these investments? 2.6 Use Formulas to Solve Word Problems

12. Example:Two search-and-rescue teams leave base at the same time looking for a lost boy. The first team, on foot, heads north at 2 mph. The other team, on horseback, south at 4mph. How long will it take them to search a distance of 21 miles between them? 2.6 Use Formulas to Solve Word Problems

13. Example:A financial planner recommends a plan for a client who has $65,000 to invest. Part of the money will be invested in a mutual fund at 12% and the remainder will be invested in municipal bonds at 6.2%. The total interest earned at the end of one year will be $6,477.60. How much will be invested at each rate? 2.6 Use Formulas to Solve Word Problems

14. Example:A teacher wants to supplement his retirement income with investment interest. If he invests $15,000 at 6% interest, how much more would he have to invest at 7% to achieve a goal of $1,250 per year in supplemental income? 2.6 Use Formulas to Solve Word Problems

15. Example:A photographer wishes to mix 2 liters of a 5% acetic acid solution with a 10% solution to get a 7% solution. How many liters of 10% solution must be added? 2.6 Use Formulas to Solve Word Problems

16. Independent Practice You learn math by doing math. The best way to learn math is to practice, practice, practice. The assigned homework examples provide you with an opportunity to practice. Be sure to complete every assigned problem (or more if you need additional practice). Check your answers to the odd-numbered problems in the back of the text to see whether you have correctly solved each problem; rework all problems that are incorrect. Read pp.163-168 and 172-179 Homework: pp.168-171 #2, 13, 15, 17, 21, 23, 37, 41, 43, 53, 57 pp.179-183 #7, 11-21 odds, 27, 29, 37, 41 2.6 More about Problem Solving