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§ 2.7

Further Problem Solving. § 2.7. Strategy for Problem Solving. General Strategy for Problem Solving UNDERSTAND the problem Read and reread the problem Choose a variable to represent the unknown Construct a drawing, whenever possible Propose a solution and check

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§ 2.7

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  1. Further Problem Solving § 2.7

  2. Strategy for Problem Solving General Strategy for Problem Solving • UNDERSTAND the problem • Read and reread the problem • Choose a variable to represent the unknown • Construct a drawing, whenever possible • Propose a solution and check • TRANSLATE the problem into an equation • SOLVE the equation • INTERPRET the result • Check the proposed solution in problem • State your conclusion

  3. Distance Problems: Finding Time When the amount in the formula is distance, we refer to the formula as the distance formula. distance = rate · time or d = r · t Example: While swimming in the ocean, Missy’s sunglasses fell off her head. If the sunglasses fall at a rate of 4 feet per second, how long will it take for them to fall 70 feet to the sand at the bottom? 1.) UNDERSTAND Let t = the time it takes the glasses to fall Continued

  4. Distance Problems: Finding Time Example continued: 2.) TRANSLATE d = rt 70 = 4t 3.) SOLVE 17.5 = t 4.) INTERPRET It will take Missy’ sunglasses 17.5 seconds to fall to the bottom. Check: rate · time = 4 · 17.5 = 70 

  5. Money Problems interest = principal · rate · time Example: Jordan invested $12,500, part at 7% simple interest and part at 6% simple interest for 1 year. How much was invested at each rate if each account earned the same interest? 1.) UNDERSTAND Let x = the amount of money invested at 7% Continued

  6. Money Problems Example continued: 2.) TRANSLATE Interest from each account is the same: I.07 = I.06 0.07x = 0.06(12500 – x) Solve the equation. Continued

  7. Money Problems Example continued: 3.) SOLVE 0.07x = 0.06(12500 – x) 0.07x = 750 – 0.06x 0.13x = 750 x = 5769.23 4.) INTERPRET Jordan deposited $5769.23 at 7% and 12500 – 2769.23 = $6730.77 at 6%. Check: Interest 7%: 5769.23(0.07) = 403.85 6%: 6730.77(0.06) = 403.85 

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