MA Lesson 11 Section 1.3. Solving Applied Problems with Linear Equations of one Variable

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Egbert Parsons
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1 MA Lesso 11 Sectio 1. I Solvig Applied Problems with Liear Equatios of oe Variable 1. After readig the problem, let a variable represet the ukow (or oe of the ukows). Represet ay other ukow usig the variable. Hit: Let your variable be the ukow you kow the least about. 2. Develop a pla; a setece or formula that relates the iformatio ad ukows.. Write a equatio that models the setece or formula. 4. Solve the equatio ad aswer the problem's questio. The variable itself may ot be the aswer or may oly be oe of the aswers. Hits: Sometimes a picture helps. Label the variable by what it represets as well as other ukows. Let your variable be the ukow you kow the least about. If a total is kow, let the variable equal part of the total ad total - variable represet the remaiig part of the total. Simple iterest: I = P r t Ex 1: Fid three cosecutive eve itegers so that the first added to twice the secod is the same as twice the third. Ex 2: A caterer charges $45 plus $8 per perso. How may persos ca Daw have at her catered dier, if she has budgeted $140? Ex : The sale price o a camera after a 20% discout is $72. What was the price before the discout? 1

2 Ex 4: There were 1200 tickets sold for a local drama club productio. Tickets brought before opeig ight cost $9 each. Tickets bought at opeig ight cost $11 each. If the productio sold out ad $11,20 reveue was collected from the sale of the tickets, how may tickets were purchased prior to opeig ight? Ex 5: Marvi took 5 tests (each out of 100 poits) durig a semester. He made the same score o the first test ad the fifth test. Scores o the secod, third, ad fourth tests were 72, 85, ad 79. If Marvi averaged 78, what was Marvi's score o the first test? Ex 6: A secod agle of a triagle is 5 more tha double a first agle. The third agle is 5 less tha triple the first agle. Fid the measure of each agle of the triagle. Hit: The sum of the agles of ay triagle is 180. Ex 7: I a certai commuity i 2005, 45% of school-aged childre had their ow cell phoes. This was icreasig by approximately.6% per year. If this tred cotiues, i what year will 99% of the school-aged childre have their ow cell phoes? 2

3 Ex 8: Oe car retal compay will ret a certai type of car for $22 a day plus $0.26 a mile. A secod car retal compay will ret the same type of car for $19 a day plus $0.28 a mile. For what daily umber of miles would the retal charges be the same? Ex 9: Fid the dimesios of a rectagle with a perimeter of 54 meters, if its legth is meters less tha twice its width. Ex 10: Tricia received a iheritace of $5500. She ivested part of it at 8% iterest ad the remider at 12% iterest. At the ed of a year, she had eared a total of $540 iterest from both accouts. How much did Tricia ivest i the 12% accout? Ex 11: Sarah ivested part of a $25,000 gift i a bak fud that eared 8% profit ad the remaider of the moey i a stock pla that lost 2 ½ %. Fid the amout of each ivestmet if her overall et profit was $

4 Ex 12: A rectagular picture measures 11 iches by 8 ½ iches ad has a picture frame of uiform width aroud it. The perimeter of the outside of the frame is 55 iches. Determie the width of the frame. There are commo geometric figure formulas listed o page 12 of the textbook. You may eed these formulas for applied problems throughout this semester. II Solvig a Formula for Oe of its Variables Solvig a formula for a variable meas rewritig the formula so that the variable is isolated o oe side of the equatio. It does ot mea obtaiig a umeral value for that variable. Ex 1: Solve y = mx + b for m Ex 14: Solve V 1 2 = π r h for h Examie the followig formula that was solved for x. Both aswers are correct. O A, both sides were divided by the coefficiet of the paretheses first, the a subtractio was performed. O B, the paretheses were cleared first, subtractio performed, the divisio. Both aswers are acceptable. Be aware o quizzes, exams, or olie homework that aswers could be give either way. A ( w + x) = 12 Solve for x. 12 w + x = 12 x = w B ( w + x) = 12 Solve for x. w + x = 12 x = 12 w 12 w x = 4

5 Ex 15: Solve 2 x( r + s) = K for r Sometime the distributive property must be used to factor out the variable beig solved for, if that variable is i more tha oe term. If the equatio ab + ac = d is solve for a, you would begi by writig a ( b + c) = d, the divide both sides by the paretheses. Ex 16: Solve y = for m Ex 17: Solve a b = c for b b b Note: If a aswer result is x =, a equivalet aswer is x =. Depedig o y c c y which side of the equatio you move the variable terms for the variable you are solvig, may determie which aswer you fid. Be aware of this. The secod expressio for x ca be foud by multiplyig the first expressio's umerator ad deomiator by 1. 5

0.07. i PV Qa Q Q i n. Chapter 3, Section 2

0.07. i PV Qa Q Q i n. Chapter 3, Section 2 Chapter 3, Sectio 2 1. (S13HW) Calculate the preset value for a auity that pays 500 at the ed of each year for 20 years. You are give that the aual iterest rate is 7%. 20 1 v 1 1.07 PV Qa Q 500 5297.01