3 Phrases to Algebraic Expressions Continuation of the translations we had in Chapter 1 and 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 number5(n – 3) The word QUANTITY means parentheses.
4 Phrases to Algebraic Expressions Example 2:½ the sum of a number and 4½ (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 number3n – “the product of 3 and a number” translates to 3n, and “14 less than…” translates to 3n – 14
5 Phrases to Algebraic Expressions Try This:3 less than twice a number ½ the difference of a number and 14 times the quantity fewer than the product of 10greater than a number and a number
6 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 = DJason’s weekly salary = 2D – “Twice David’s weekly salary” translates to 2D and 35 less than… translates to D – 35Try 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.
7 Using Equations to Solve Problems Remember the problem solving guidelinesUnderstand the problemWhat am I trying to find?What data am I given?Have I even solved a similar problem?Develop and carry out a PLANWhat strategies might I use to solve the problem?How can I correctly carry out the strategies I select?Find the Answer and CheckDoes the proposed solution check?What is the answer to the problem?Does the answer seem reasonable?Have I stated the answer clearly?
8 Example 5The 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 ProblemQuestion: 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 planLet b = the number of boys in the band2b + 6 = the number of girls in the band
9 Example 5 Develop and carry out a plan Let b = the number of boys in the band2b + 6 = the number of girls in the band b + 6 = 882b = 82B = 41Find the answer and checkThere are 41 boys in the band. To check plug 41 back into the equation2(41) + 6 = 88= 8888 = 88
10 Example 6Kara 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 problemQuestion: 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 planLet h = the number of additional hours she must drive55h = the additional distance she must travel
11 Example 6 Develop and carry out a plan Let h = the number of additional hours she must drive55h = the additional distance she must travel55h + 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 equation55h + 75 = 35055 h = 275h = 5
12 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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