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2-9 Writing Equations

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Write an Equation We covered the Problem solving guidelines back in chapter 1. Problem Solving Guidelines Phase 1: Understand the problem What am I trying to find? What data am I given Have I ever solved a similar problem Phase 2: Develop and carry out a PLAN What strategies might I use to solve the problem How can I correctly carry out the strategies I selected Phase 3: Find the Answer and Check Does the proposed solution check? What is the answer to the problem? Does it seem reasonable? Have I stated the answer clearly?

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Write an Equation Here are some tips you can use when your plan involves writing an equation. Planning to write and solve an equation Can I use a variable to represent an unknown number? Can I represent other conditions in terms of the variable? Can I find equivalent expressions? Can I write and solve an equation?

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Example 1 Which equation can be used to solve the problem? Jose’s salary this year was $23,400. This is $1700 more than he made last year. What was his salary last year? (A) l – 1700 = 23,400 (B) 1700 + l = 23,400 (C) l = 23,400 – 1700 Understand the Problem Question: What was Jose’s salary last year? Data: Jose earned $23,400 this year. This is $1700 more than last year. Develop a plan Let l = last years salary Our data tells us that 23,400 is 1700 more than l. This is the same as equation (B). We can also say that last years salary was 1700 less than this years salary. This is the same as equation (c). Either B or C are correct equations

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Example 1 Our data tells us that 23,400 is 1700 more than l. This is the same as equation (B). We can also say that last years salary was 1700 less than this years salary. This is the same as equation (c). Either B or C are correct equations Find answer and check Either (B) 1700 + l = 23,400 or (C) l = 23,400 – 1700 are correct equations. If this is true we should come up with the same answer for both equations (B) (C) 1700 + l = 23,400 l = 23,400 - 1700 -1700 - 1700 l = 21,700 l = 21,700 Both equations give us the same solution so 21,700 is Jose’s salary last year.

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Example 2 Write an equation that could be used to solve the problem. A color television set uses about 420 kilowatt hours (k Wh) of electrical energy in a year. That is 3.5 times the amount of energy used by a black-and-white set. How many k Wh does a black and white set use in a year? Understand the Question Question: How many k Wh does a black and white set use in a year? Data: A color set uses 420 k Wh. a year. This is 3.5 times as much as the amount used by a black and white set. Develop and carry out a plan Let b = number of k Wh used by a black and white set. 3.5b = number of hours used by a color set (3.5)b = 420

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Example 2 (3.5)b = 420 b = 420 b = 120 k Wh 3.5 Find the answer and check 120 is the kilowatt hours used by a black and white television Check: (3.5)120 = 420 420 = 420

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Example 3 Write an equation that could be used to solve the problem In baseball, a player’s batting average multiplied by the number of times at bat equals the number of hits. A player had 125 at-bats and 36 hits. What was this players batting average? Understand the Question Question: What was this players batting average? Data: A player had 125 at-bats and 36 hits Develop and Carry out a plan Let b = players batting average 125b = number of players hits after 125 at bats (125)b = 36

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Example 3 (125)b = 36 b = 36 b =.288 125 Find answer and Check.288 is the players batting average after 125 at bats. (125)(.288) = 36 36 = 36 The answer checks.

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