8.2 Problem Solving with Proportions

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Presentation transcript:

8.2 Problem Solving with Proportions How to use the properties of proportions. How to use a problem-solving plan for problems that can be solved by proportions.

8.2 Problem Solving with Proportions Additional Properties of Proportions 3. If , then . Interchange Means Property 4. If and only if .

8.2 Problem Solving with Proportions How would you and your partner prove property #3? (a, b, c and d are nonzero.) If Why ? Hint: Multiply both sides by .

8.2 Problem Solving with Proportions Using Properties of Proportions The ratio of the width of the blue rectangle to its length is equal to the ratio of the width of the red rectangle to its length. If squares are adjoined to each rectangle, will the width-to-length ratios of the new rectangles be equal? b d a c Property 4 of proportions b d Reciprocal property The width to length ratios of the new rectangles are equal.

8.2 Problem Solving with Proportions A Problem-Solving Plan Ask yourself what you need to know to solve to the problem. Then : Write a verbal model that will give you what you need to know. Assign labels to each part of your verbal model. Write an algebraic model, using your labels and based on your verbal model. Solve the equation or inequality (the algebraic model). Answer the original question. Check that your answer is reasonable.

8.2 Problem Solving with Proportions Suppose you and your math partner are driving from Columbia, South Carolina to Boise, Idaho, a trip of about 2000 miles. You began with a full tank of gas. After driving 380 miles, you stop for gas. It takes 14 gallons to fill the tank, and the gas costs $1.25 per gallon. How much should you plan to spend on fuel for the remainder of the trip? Verbal Model Fuel cost for 2000 miles Fuel cost for 380 miles 2000 miles 380 miles = Fuel cost for 2000 miles is = x Fuels cost for 380 miles is = (14)(1.25) Labels Algebraic Model

8.2 Problem Solving with Proportions The gear ratio of two gears is the ratio of the number of teeth of the larger gear to the number of teeth of the smaller gear. For the gears shown in the example below, the ratio of Gear A to Gear B is equal to the ratio of Gear B to Gear C. Gear A has 18 teeth and Gear C has 8 teeth. Can you and your partner determine how many teeth Gear B has? Number of teeth For Gear A_____ Number of teeth For Gear B_____ Verbal Model ________________ ______________ = = Number of teeth For Gear B Number of teeth For Gear C Labels Number of teeth for Gear A = 18 Number of teeth for Gear C = 8 Number of teeth for Gear B = x Algebraic Model Cross Product Property Positive square root

8.2 Problem Solving with Proportions Homework:382/1 – 29, skip 24