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Answers pg ) 8 4) 9 6) 3 8) 11 10) -9 12) ) 19 16) 5 18) 4 20) 16 22) -4 24) 3 26) -20

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3-4 Expressions and Equations

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Phrases to Algebraic Expressions Continuation of the translations we had in Chapter 1 and 2. We know that “five more than a number” translates to “ n + 5”. Now we are going to learn about more difficult translations. Remember the key words chart from chapter 1. Example 1: 5 times the quantity 3 less than a number 5(n – 3) - The word QUANTITY means parentheses.

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Phrases to Algebraic Expressions Example 2: ½ the sum of a number and 4 ½ (n + 4) - the sum of a number and 4, translates to ( n + 4), ½ the sum translates to ½ ( n + 4) Example 3: 14 less than the product of 3 and a number 3n – 14 - “the product of 3 and a number” translates to 3n, and “14 less than…” translates to 3n – 14

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Phrases to Algebraic Expressions Try This: 3 less than twice a number ½ the difference of a number and 1 4 times the quantity 3 2 fewer than the product of 10 greater than a number and a number

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Phrases to Algebraic Expressions Example 4: Jason’s weekly salary is $35 less than twice David’s weekly salary. Let D = David’s weekly salary in dollars. Write an expression, using D, for Jason’s weekly salary. David’s weekly salary = D Jason’s weekly salary = 2D – 35 “Twice David’s weekly salary” translates to 2D and 35 less than… translates to 2D – 35 Try This: This year Todd sold five fewer houses than twice as many as he sold last year. Let n = the number he sold last year. Write an expression for the number of houses that Todd sold this year.

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Using Equations to Solve Problems Remember the problem solving guidelines Understand the problem What am I trying to find? What data am I given? Have I even solved a similar problem? Develop and carry out a PLAN What strategies might I use to solve the problem? How can I correctly carry out the strategies I select? Find the Answer and Check Does the proposed solution check? What is the answer to the problem? Does the answer seem reasonable? Have I stated the answer clearly?

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Example 5 The number of girls in the band is 6 more than twice the number of boys. There are 88 girls in the band. How many boys are in the band? Understand the Problem Question: How many boys are in the band? Data: The number of girls is 6 more than twice the number of boys; 88 girls are in the band. Develop and carry out a plan Let b = the number of boys in the band 2b + 6 = the number of girls in the band

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Example 5 Develop and carry out a plan Let b = the number of boys in the band 2b + 6 = the number of girls in the band 2b + 6 = b = B = 41 Find the answer and check There are 41 boys in the band. To check plug 41 back into the equation 2(41) + 6 = = = 88

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Example 6 Kara has driven 75 miles. She averages 55 mi/h. How many more hours must Kara drive to travel a total of 350 miles. Understand the problem Question: How many additional hours must Kara drive? Data: She averages 55 mi/h; she has already traveled 75 miles; she wants to travel a total of 350 miles. Develop and carry out a plan Let h = the number of additional hours she must drive 55h = the additional distance she must travel

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Example 6 Develop and carry out a plan Let h = the number of additional hours she must drive 55h = the additional distance she must travel 55h + 75 = the total distance of the trip ; Since 55h + 75 represents the total distance for the trip, and we know that the total distance is 350 miles, we have the equation 55h + 75 = h = h = 5

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Example 6 Find the answer and check Kara must drive for 5 more hours. 5 (55) = 275 miles. This plus 75 miles gives the total of 350 miles. This answer checks. Try This: When Jill sells 2 more buckets, she will have sold 3 times as many buckets as Jack sold. Jill has sold 19 buckets. How many buckets has Jack sold? An 18-mile section of highway is being paved. The first 3 miles are done. The same number of miles will be paved each day. How many miles should be paved each day to complete this section in the next 10 days?

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Homework Page – 16 ALL 22 – 24 ALL

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