§ 2.7 Further Problem Solving

Martin-Gay, Beginning and Intermediate Algebra, 4ed 22 Strategy for Problem Solving General Strategy for Problem Solving 1)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 2)TRANSLATE the problem into an equation 3)SOLVE the equation 4)INTERPRET the result Check the proposed solution in problem State your conclusion

Martin-Gay, Beginning and Intermediate Algebra, 4ed 33 Distance Problems: Finding Time distance = rate · time or d = r · t When the amount in the formula is distance, we refer to the formula as the distance formula. 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? Continued 1.) UNDERSTAND Let t = the time it takes the glasses to fall

Martin-Gay, Beginning and Intermediate Algebra, 4ed 44 Distance Problems: Finding Time 17.5 = t Check: rate · time = 4 · 17.5 = 70 Example continued: 2.) TRANSLATE d = rt 70 = 4t 3.) SOLVE 4.) INTERPRET It will take Missy’ sunglasses 17.5 seconds to fall to the bottom.

Martin-Gay, Beginning and Intermediate Algebra, 4ed 55 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? Continued 1.) UNDERSTAND Let x = the amount of money invested at 7%

Martin-Gay, Beginning and Intermediate Algebra, 4ed 66 Money Problems Example continued: 2.) TRANSLATE principal · rate · time = interest AccountPrincipalRateTimeInterest 7% Account x x 6% Account – x (12500 – x) Interest from each account is the same: I.07 = I x = 0.06(12500 – x) Solve the equation. Continued

Martin-Gay, Beginning and Intermediate Algebra, 4ed 77 Money Problems Example continued: 3.) SOLVE 4.) INTERPRET 0.07x = 0.06(12500 – x) 0.07x = 750 – 0.06x 0.13x = 750 x = Jordan deposited $ at 7% and – = $ at 6%. Check: Interest 7%: (0.07) = %: (0.06) =