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Algebra – 2.15

Algebra – 2.15. Building Equations. GUESS-CHECK-GENERALIZE. This is a method that we use for solving word problems. GUESS: make guesses (they don’t have to be good guesses) CHECK: use math to check if your guess is correct

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Algebra – 2.15

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  1. Algebra – 2.15 Building Equations

  2. GUESS-CHECK-GENERALIZE • This is a method that we use for solving word problems. • GUESS: make guesses (they don’t have to be good guesses) • CHECK: use math to check if your guess is correct • GENERALIZE: use the same steps to check if some guess ‘x’ is correct, and use this to solve

  3. Remember this problem? • Vanessa works 32 hours per week at her job. Her boss offers her a full-time position (40 hours a week) and a $2-per-hour raise. She says, “Super! Now I’ll make $200 more a week!” What was her hourly wage before the raise?

  4. GUESS-CHECK • First, guess what the hourly wage was before the raise. • *You’re not trying to get the right answer right now, you’re just trying to learn how to check a guess. • Check your guess. Keep track of the steps that you take. • Repeat with another guess. Keep guessing until the checking becomes automatic.

  5. GENERALIZE • Make your guess a variable. • Take the same steps that you used before.

  6. Some practice • Ancient Egyptian mathematicians used the concept of “false position” to solve equations. You guess a convenient answer and then adjust it to find the correct answer. • Example: A number plus one fourth of itself equals 210. What is the number? • A convenient guess is 4. Why is this convenient? • Suppose you guess 4. What is the result of adding one fourth of 4 to itself? • Guess 12. How does the result of the same calculation compare to the result with 4? • Use the GCG method to solve the problem.

  7. Last summer, Katie mowed lawns to earn money. She mowed 35 lawns per week and charged $6 per lawn. This summer, Katie wants to earn an additional $150 per week. She will raise her price to $8 and find more customers. • If Katie finds 4 new customers and still keeps her former customers, will she earn an additional $150 a week? • If Katie finds 13 new customers, will she earn an additional $150 a week? • If Katie finds 8 new customers, will she earn an additional $150 a week? • Use GCG to build an equation for finding the number of new customers Katie needs to earn $150 extra. • Solve the equation.

  8. Suppose Katie charges $9 per lawn. How many new customers must she find in order to make an extra $150 a week?

  9. In 36 years, Anna will be five times as old as she is today. How old is Anna?

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