Applied (Word) Problems NoteSheet Consecutive Integers ...

1 Applied (Word) ProblemsNoteSheetConsecutiv eIntegersConsecutivenumbers(ormoreproper ly,consecutiveintegers)areintegersnrandn gsuchthat/h - nl = I, ,IJlfollowsimmediatelyafter17,.Giventwoc onsecutivenumbers, anevennumberandanoddnumberis alwaysodd,thesumof twoconsecutivenumbers(and,infact,of anynumberof consecutivenumbers)is n is aninteger,thenn, n+ 1, andn+ 2 wi II :1,2,3,4,5-3,-2,-1,0,1,21004,1005, differenceof n is aninteger,then2n+1, 2n+3, and2n+ :3,5,7,9-23,-21,-19,-17,-15,-13,-11123,1 25,127, n is aninteger,then2n, 2n+2,and2n+ :4,6,8,10-2,0,2,4,6-120,-118,-116J. GrossmanApplied (Word) ProblemsNoteSheetCo nsecutiveIntegersExample1: ConsecutiveIntegerProblemThesumof theleastandgreatestof 3 consecutiveintegersis the3integers?

2 Solution:Step1: Assignvariables:Letx = leastintegerx + 1 = middleintegerx + 2 = greatestintegerTranslatesentenceintoan :Thesumof theleastandgreatestis :x + (x + 2) = 60 Step2: SolvetheequationCombineliketerms:2x + 2 = 60 Isolatevariablex: 2x =5858X=-=292 Step3: Checkyouranswer:29+ 29+ 2 = 60 Thequestionwantsallthe3 consecutivenumbers:29,30and3]Answer:The3 consecutivenumbersare29, : ConsecutiveOddIntegerProblemThelengthsof thesidesof a thelengthof thelongestsideif theperimeteris 45?Solution:Step1: Beingconsecutiveoddnumbersweneedto add2 to :Letx = lengthof shortestsidex + 2 = lengthof mediumsidex + 4 = lengthof longestsideJ. GrossmanApplied (Word) ProblemsNoteSheetCo nsecutiveIntegersSketchthefigurexx +2x+4 Step2: Writeouttheformulaforperimeterof = sumof the threesidesStep3: Plugin x + x + 2 + x + 4 Combineliketerms:45= 3x + 6 Isolatevariablex: 3x = 45- 63x = 39x=13 Step3: Checkyouranswer13+13+2+13+4=45 Becareful!

3 Thequestionrequiresthelengthof longest= 13 + 4 =17 Answer:Thelengthof longestsideis 17 Example3: ConsecutiveEvenIntegerProblemTwoconsecut iveevennumbershavea sumof :Step1: Beingconsecutiveevennumbersweneedto add2 to :Letx = smallestconsecutiveintegerx + 2 = middleor nextconsecutiveevenintegerx + 4 = largestconsecutiveevenintegerStep2: Writeouta formula:x + (x + 2) + (x+4)= 30 Step3: SolvetheequationCombineliketerms:3x + 6 = 30 Isolatevariablex: 3x = 24x=8 Step4: Plugin valuesandcheckyouranswer:8 + 10+12 = 30 Thequestionwantsallthe3 :8, 10, GrossmanApplied (Word) ProblemsConsecutive IntegerandNumberProblemsCONSECUTIVEINTEG ERPROBLEMS1. Findtwoconsecutiveintegerswhosesumis Findtwoconsecutiveintegerswhosesumis Findthreeconsecutiveintegerswhosesumis Findthreeconsecutiveintegerswhosesumis -545.

4 Findtwoconsecutiveevenintegerswhosesumis 546. Findtwoconsecutiveevenintegerswhosesumis -387. Findthreeconsecutiveevenintegerswhosesum is 848. Findthreeconsecutiveevenintegerswhosesum is -489. Findtwoconsecutiveoddintegerswhosesumis thefirstandthethirdis 14 thefirstandsecondis thesmallestand3 timesthesecondis :1. When4 timesa numberis increasedby40,theansweris thesameas when100is decreasedby When7 timesa numberis decreasedby8, theansweris thesameas when3 timesthenumberis increasedby 4. GrossmanApplied (Word) ProblemsConsecutive IntegerandNumberProblems3. Eighttimesa numberincreasedby9 is thesameas 15 morethan7 Thirtydecreasedby6 timesa numberis thesameas 16 When6 timesa numberis increasedby11 theresultis 16 lessthan9 Onenumberis the12 is subtractedfromthelargernumbertheresultis 7 Thelargerof twonumbersis 10 If 13 is addedto a numberandthesumis multipliedby3, theresultis 7 timesthenumberdecreasedby9.

5 Thesumof twonumbersis thelargerof thetwonumbersis 9 lessthantwicethesmaller, twonumbersis 4 pieceof lumberwhichis 55incheslongis cutintotwopartssuchthat2 timesthelargerpartwillbe12 morethan5 thepiecesoflumber? twonumbersis 6 lessthan3 7 morethan4 twonumbersis 7 twonumbersis 18 5 timesthelargernumberexceeds4 pieceof fabric180incheslongis cutintotwopiecessuchthat3 ti mesthelargerpieceexceeds4 fabric?J. Grossman"..J fl ~!D~!D~~DJ1)~DdD~J{~k~~Solveeachproblem, thencrossouttheletternexttothecorrect ~ ,.theanswertothetitlequestionwillremain. z -57, ,60::)-13,-11,-9I&.16,17,18077,79:z:U44, 46,48fII54,561&172,74,76Z42,440a -11,-9,-7o Findtwoconsecutiveintegerswhosesumis 75.}

6 E Findthreeconsecutiveintegerswhosesumis Findthreeconsecutiveintegerswhosesumis Findtwoconsecutiveevenintegerswhosesumis Findthreeconsecutiveevenintegerswhosesum is Findtwoconsecutiveoddintegerswhosesumis Findfourconsecutiveoddintegerswhosesumis Findtwoconsecutiveevenintegerssuchthatth esumof thelargerand3 timesthesmalleris 234. 17,18,19037,38e Findtwoconsecutiveoddintegerssuchthatthe sumofthesmallerand3 timesthelargeris ,83cc68,70,72eFindthreeconsecutiveintege rssuchthatthesumofthelargestand5 timesthesmallestis -244.:E48,50,52 -39,-38,-37 GFindthreeconsecutiveevenintegerssuchtha tthesumCCof twicethesmallestand4 timesthelargestis 304.:z:eFindthreeconsecutiveoddintegerss uchthatthesum~ -59, 7 timesthesmallestandtwicethelargestis :SolvingProblemsInvolvingConsecutiveInte gersPUNCHLINE Algebra BookA