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Sullivan Algebra and Trigonometry: Section 1.2

Sullivan Algebra and Trigonometry: Section 1.2. Objectives of this Section Translate Verbal Descriptions into Mathematical Expressions Set Up Applied Problems Solve Interest Problems Solve Mixture and Motion Problems Solve Constant Rate Job Problems. English. Math Translation.

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Sullivan Algebra and Trigonometry: Section 1.2

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  1. Sullivan Algebra and Trigonometry: Section 1.2 • Objectives of this Section • Translate Verbal Descriptions into Mathematical Expressions • Set Up Applied Problems • Solve Interest Problems • Solve Mixture and Motion Problems • Solve Constant Rate Job Problems

  2. English Math Translation is, are, was = of Multiplication 5 more than a number 5 + x 8 less than a number x - 8 The quotient of a number and 6 x / 6 3 times a number 3x Translating English into Math: Examples

  3. Steps for Setting Up Applied Problems Step 1: Read the problem carefully, perhaps two or three times. Identify what you are looking for. Step 2: Assign a letter (variable) to represent what you are looking for. Express any remaining unknown quantities in terms of that variable. Step 3: Make a list of known facts and translate them into mathematical expressions. These may take the form of an equation or later, an inequality. Step 4: Solve the equation for the variable and answer the question using a sentence. Step 5: Check your answer with the facts of the problem.

  4. Example: Yolanda, Mary, and Sophie won $200,000 playing the lottery. Based on how much each contributed to buy the ticket, Mary gets four fifths of what Yolanda gets, while Sophie gets three fourth of what Mary gets. How much does each receive?

  5. Example: The suggested list price of a new car is $16,000. The dealer cost is 80% of list. How much will you pay if the dealer is willing to accept $2000 over the cost for the car? x: cost to you y: cost to the dealer

  6. Example: The purity of gold is measured in karats, with pure gold being 24 karats. Other purities of gold are expressed as proportional parts of pure gold. Thus, 18 karat gold is 18/24, or 75% pure gold. How much 12 karat gold should be mixed with 18 karat gold to obtain 50 grams of 14 karat gold?

  7. Hours to do job Fraction of Job Done in 1 Hour Jeff 3 1 / 3 Melissa 2 1 / 2 Together t 1 / t Example: Jeff can mow his lawn in 3 hours. Melissa can mow the same lawn in 2 hours. Working together, how long will the job take, assuming that there is no gain or loss of efficiency working together. t: hours needed to complete the job together

  8. Part done by Jeff in 1 hour Part done by Melissa in 1 hour + = Part done together in 1 hour

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