<p>Math 170 - Cooley Pre-Calculus OCC</p><p>Section 1.2 – Constructing Models to Solve Problems Definition – Function A function is a rule for determining the value of one variable from the values of one or more other variables. We say that the first variable is a function of the other variable(s). Strategy – Problem Solving 1. Read the problem as many times as necessary to get an understanding of the problem. 2. If possible, draw a diagram to illustrate the problem. 3. Choose a variable, write down what it represents, and if possible, represent any other unknown quantities in terms of that variable. 4. Write an equation that models the situation. You may be able to use a known formula, or you may have to write an equation that models only that particular problem. 5. Solve the equation. 6. Check your answer by using it to solve the original problem (not just the equation). 7. Answer the question posed in the original problem.  Exercises:</p><p>Solve each formula for the specified variable..</p><p>1 1 1 1 1 1) A= bh for h (area of a triangle) 2) = + + for R1 (resistance) 2 R R1 R 2 R 3</p><p>Solve each problem.</p><p>3) Julia’s soybean field is 3 m longer than it is wide. To increase her production, she plans to increase both the length and width by 2 m. If the new field is 46 m2 larger than the old field, then what are the new dimensions of the old field?</p><p>1 Math 170 - Cooley Pre-Calculus OCC</p><p>Section 1.2 – Constructing Models to Solve Problems  Exercises:</p><p>Solve each problem.</p><p>4) A pharmacist needs to obtain a 70% alcohol solution. How many ounces of a 30% alcohol solution must be mixed with 40 ounces of an 80% alcohol solution to obtain a 70% solution?</p><p>5) Boudreaux rowed his pirogue from his camp on the bayou to his crab traps. Going down the bayou, he caught a falling tide that increased his normal speed by 2 mph, but coming back it decreased his normal speed by 2 mph. Going with the tide, the trip took only 10 min; going against the tide, the trip took 30 min. How far is it from Boudreaux’s camp to his crab traps?</p><p>6) Della can scrape the barnacles from a 70-ft yacht in 10 hr using an electric barnacle scraper. Don can do the same job in 15 hr using a manual barnacle scraper. If Don starts scraping at noon and Della joins him at 3 P.M., then at what time will they finish?</p><p>7) How many quarts of a 20% alcohol solution and how many quarts of pure alcohol solution should be mixed together to obtain 100 quarts that contain 30% solution?</p><p>2</p>