1.3 Models & Applications
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1 GOALS: 1. Translate word problems to algebra. 2. Solve word problems using a systematic approach. 3. For equations with more than one variable, solve for one of the variables in terms of the other. Study 1.3 CVC 1 7 # 1 11; 15, 19, 23,... 43; 49, 53, 57..., 69 Problem: Statistics indicate that, in your life: You will devote 32 years to sleeping and eating. The number of years sleeping will exceed the number of years eating by 24. How many years will you spend sleeping? How many years eating? How do we solve such problems? Need to translate words > algebra use algebra > solution G. Battaly
2 Start small: When two times a number is decreased by 3, the result is 11. Find the number. Start small: When two times a number is decreased by 3, the result is 11. Find the number. translate words > algebra let x = the number then 2x 3 = 11 G. Battaly
3 Start small: When two times a number is decreased by 3, the result is 11. Find the number. translate words > algebra use algebra > solution let x = the number then 2x 3 = 11 2x = 14 x = 7 Check: 2(7) = 14, 14 3 = 11 One number exceeds another by 24. The sum of the two numbers is 58. Find the numbers. G. Battaly
4 One number exceeds another by 24. The sum of the two numbers is 58. Find the numbers. let x = the 2nd number then x + 24 = 1st number x + (x + 24) = 58 solve: 2x + 24 = 58 2x = 34 x = 17 2nd # x + 24 = 41 1st # Problem: Statistics indicate that, in your life: You will devote 32 years to sleeping and eating. The number of years sleeping will exceed the number of years eating by 24. How many years will you spend sleeping? How many years eating? G. Battaly
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