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Thinking Mathematically

This guide focuses on applying linear equations to solve word problems effectively. It outlines a clear strategy starting from understanding the problem and expressing unknowns using variables. Key steps include reading the problem thoroughly, defining relevant variables, formulating equations based on verbal conditions, solving these equations, and validating the solutions. Examples of practical applications, such as finding the depreciation of an asset or comparing costs, are included to illustrate techniques in real-life scenarios. Master these strategies to simplify and solve math problems efficiently.

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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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