ISBN Copyright 2015 The Continental Press, Inc.

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1 TABLE OF CONTENTS Itroductio 3 Format of Books 4 Suggestios for Use 7 Aotated Aswer Key ad Extesio Activities 9 Reproducible Tool Set 183 ISBN Copyright 2015 The Cotietal Press, Ic. Exceptig the desigated reproducible blacklie masters, o part of this publicatio may be reproduced i ay form or by ay meas, electroic, mechaical, photocopyig, recordig, or otherwise, without the prior writte permissio of the publisher. All rights reserved. Prited i the Uited States of America.

10 Solvig Problems with Proportioal Relatioships PAGES 78 AND 79 Objective To use proportios to solve real-world percet problems, icludig discouts ad tax 1 Itroductio Review that a percet is a ratio

2 10 Solvig Problems with Proportioal Relatioships PAGES 78 AND 79 Objective To use proportios to solve real-world percet problems, icludig discouts ad tax 1 Itroductio Review that a percet is a ratio that compares a umber to. Discuss problem situatios where percets are used: fidig a percet of a umber, fidig what percet oe umber is of aother, ad fidig the whole whe a percet is kow. The work through the examples that show how to set up a represetative proportio ad solve for the ukow to fid a percet of a umber ad to fid the percet oe umber is of aother. Be sure studets uderstad that oe ratio of the proportio will always be some umber to, which represets the percet. Thik About It Studets should recogize that if a discout is 40% of the origial price, the the sale price is the remaiig amout, which is 60% of the origial price. Either 40% ca be subtracted from $160 or 60% of $160 ca be foud. 15, , cross multiplicatio Commo Core State Stadard Use proportioal relatioships to solve multistep ratio ad percet problems ,500,000 Divide both sides of the equatio by the coefficiet of the variable, 25. $60,000 Vocabulary percet: a ratio that compares a umber to, writte with the symbol % 8 24, UNIT 2 The Cotietal Press, Ic. DUPLICATING THIS MATERIAL IS ILLEGAL.

3 PAGES 80 AND 81 LESSON 10 SOLVING PROBLEMS WITH 24, , ,000 Divide both sides by. $2,000 50% $1,920 2 Focused Istructio First, studets are give a percet ad its value ad asked to fid the whole. Questios guide them i settig up the two ratios of the proportios; studets recogize that 15,000 represets the amout of tax paid o a icome of dollars, ad this is equivalet to 25. They cross multiply to achieve a equatio that they ca solve for the ukow. Next, studets idetify a discout as a percet of a umber. They use this uderstadig to set up ratios ad a proportio that ca be solved to fid the amout of the discout. Coclude the Focused Istructio sectio by havig studets solve two problems ivolvig percets ; ; Guided Practice Studets should complete the Guided Practice sectio o their ow. Offer assistace as eeded, poitig out the remider ad hit boxes alog the right side of the page. 50 $ ; 5 6,000; ; 5 1,120; Coectios to Stadards for Mathematical Practice Make sese of problems ad persevere i solvig them. Reaso abstractly ad quatitatively. Model with mathematics. Atted to precisio. Look for ad make use of structure. The Cotietal Press, Ic. DUPLICATING THIS MATERIAL IS ILLEGAL. UNIT 2 49

4 LESSON 10 SOLVING PROBLEMS WITH PAGES 82 AND 83 4 Idepedet Practice Aswer Ratioales 1 Because all the ratios are equal, ay oe of them ca be used to set up the discout proportio. For example, Cross multiplyig results i Divide both sides of the equatio by 5 to solve: , ad 5 25 or %. Choice B is correct. Choice A is half of the discout percet, ad choices C ad D are too large. 2 A Both ratios i the proportio compare the umber of seats filled to the total umber of seats: B Cross multiply to solve for : ,000. Divide both sides of the equatio by 75: 5 15, There are 200 seats i the 75 theater ; ,000; The proportio uses ratios that compare the commissio to the total, 180, Cross multiply for 5 720,000. Divide both sides by, ad 5 7,200. The commissio is $7,200; choice B is correct. Choice A divides 180,000 by 4 istead of multiplyig the two umbers. Choice C divides istead of multiplies ad has the decimal poit i the wrog place. Choice D has the decimal i the wrog place. 4 The ratio used to solve the problem is Solvig for, , so , ad The actual car is 120 iches log. Sice the questio asks for the legth i feet, divide the legth i iches by 12 for 10 feet. 5 S A ad B A tax is a percet of a umber, i this case, the cost of the televisio. The proportio that represets this situatio is First cross multiply: 1, The divide both sides by 250 for The tax rate is 6.5% First I wrote a proportio with the ratio of tax to cost o oe side, , ad a ratio of ukow percet to o the other,. I cross multiplied to get 1, , ad the solved for. 50 UNIT 2 The Cotietal Press, Ic. DUPLICATING THIS MATERIAL IS ILLEGAL.

5 PAGE 84 LESSON 10 SOLVING PROBLEMS WITH 18, , ; 5 112,500; 5 1,125 6 A A amout of simple iterest is a percet of a umber. The proportio that represets this situatio is 18, B To solve for the amout of iterest, first cross multiply: 112, Divide both sides of the equatio by : 1, The amout of simple iterest is $1,125. 1,125 Extesio Activity Prepare a spier divided ito 20 equal sectios, ad label the sectios with percetages i icremets of 5 from 5% to %. Ask studets to brig i a advertisemet or a pritout from a website of a item they would like to buy; it should display a udiscouted price. Let each studet spi the arrow to fid a discout percet for his or her item. Have the studet demostrate how to set up a proportio with the percet as oe ratio ad the price i the other, ad the fid the equatio ad solve for the amout of discout. Studets may wat to take this a step further ad fid the price after the discout. The Cotietal Press, Ic. DUPLICATING THIS MATERIAL IS ILLEGAL. UNIT 2 51

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

MA Lesson 11 Section 1.3. Solving Applied Problems with Linear Equations of one Variable MA 15200 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