Applications: Interest, Mixture, Uniform Motion, Constant Rate Jobs OBJECTIVES: Translate Verbal Descriptions into Mathematical Expressions Solve Application Word problems

Steps for Setting up Applied Problems Read the problem carefully, perhaps two or three times. Pay particular attention to the question being asked in order to identify what you are looking for. If you can, determine realistic possibilities for the answer. Attempt to state the problem in your own words. Assign a letter (variable) to represent what you are looking for, and if necessary, express any remaining unknown quantities in terms of this variable. Make a list of all the known facts and translate them into mathematical expressions. These may take the form of an equation (or, later, an inequality) involving the variable. If possible, draw an appropriately labeled diagram to assist you. Sometimes a table or chart helps. Solve the equation for the variable and then answer the question. Check the answer with the facts in the problems. If it agrees, congratulations!! If it does not agree, try again. Steps for Setting up Applied Problems

Interest formula: Interest equals principle times interest rate times time Mixture problems: Price per unit times number of units equals total cost Uniform motion: Distance equals average velocity times time Constant Rate Jobs: Part of job done by one person plus part of job done by another person equals part of job done together Applied Problems

Solve the applied problems FINANCIAL PLANNING: Betsy, a recent retiree, requires $6000 per year in extra income. She has $50,000 to invest and can invest in B-rated bonds paying 15% per year or in a certificate of deposit (CD) paying 7% per year. How much money should be invested in each to realize exactly $6000 in interest per year? Solve the applied problems

Solve the applied problems BLENDING TEAS: The manager of a store that specializes in selling tea decides to experiment with a new blend. She will mix some Earl Grey tea that sells for $5 per pound with some Orange Pekoe tea that sells for $3 per pound to get 100 pounds of the new blend. The selling price of the new blend is to be $4.50 per pound, and there is to be no difference in revenue from selling the new blend versus selling the other types. How many pounds of the Earl Grey tea and Orange Pekoe are required? Solve the applied problems

Solve the applied problems MIXING WATER AND ANTIFREEZE: The cooling system of a certain foreign-made car has a capacity of 15 liters. If the system is filled with a mixture that is 40% antifreeze, how much of this mixture should be drained and replaced by pure antifreeze so that the system is filled with a solution that is 60% antifreeze? Solve the applied problems

Solve the applied problems PHYSICS: UNIFORM MOTION A motorboat maintained a constant speed of 15 miles per hour relative to the water in going 10 miles upstream and then returning. The total time for the trip was 1.5 hours. Use this information to find the speed of the current. Solve the applied problems

Solve the applied problems WORKING TOGETHER ON A JOB: Trent can deliver his newspapers in 30 minutes. It take Lois 20 minutes to do the same route. How long would it take them to deliver the newspapers if they work together? Solve the applied problems

GOOD LUCK! GOOD LUCK! RECALL words of translation REMEMBER to read the problem as many times as needed and try to sort the important information from the junk NEVER forget to TRY and TRY AGAIN until you succeed. GOOD LUCK! GOOD LUCK!