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Thinking Mathematically

Thinking Mathematically. Algebra: Equations and Inequalities 6.3 Applications of Linear Equations. Algebraic Translations of English Phrases. See Table 6.2 Examples 8 is decreased by 5 times a number The quotient of 15 and a number The sum of twice a number and 20

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Thinking Mathematically

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  1. Thinking Mathematically Algebra: Equations and Inequalities 6.3 Applications of Linear Equations

  2. Algebraic Translations of English Phrases See Table 6.2 Examples 8 is decreased by 5 times a number The quotient of 15 and a number The sum of twice a number and 20 30 subtracted from 7 times a number

  3. Strategy for Solving Word Problems Before you start: Read the problem carefully at least twice. Attempt to state the problem in your own words and state what the problem is looking for. Step 1: Let x (or any variable) represent one of the quantities in the problem. Step 2: If necessary, write expressions of any other unknown quantities in the problem in terms of x. Step 3: Write an equation in x that describes the verbal conditions of the problem.

  4. Strategy for Solving Word Problems Step 4: Solve the equation and answer the problem’s question. Step 5: Check the solution in the original wording of the problem, not in the equation obtained from the words.

  5. Examples: Word Problems Exercise Set 6.3 #9, 29 • One number exceeds another by 26. The sum of the numbers is 64. What are the numbers. • A new car worth $24,000 is depreciating n value by $3,000 per year. After how many years will the car’s value be $9,000?

  6. Examples: Word Problems Exercise Set 6.3 #33, 39 • The bus fare in a city is $1.25. People who use the bus have the option of purchasing a monthly coupon book for $15.00. With the coupon book, the fare is reduced to $0.75. Determine the number of times in a month the bus must be used so that the total monthly cost without the coupon book is the same as the total monthly cost with the coupon book. • After a 20% reduction, you purchase a television for $336. What was the television’s price before the reduction?

  7. Thinking Mathematically Algebra: Equations and Inequalities 6.3 Applications of Linear Equations

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