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.
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
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
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.
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?
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
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
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
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
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?