ࡱ> RTQ'` bjbj .$LLLLLLL``$N<XPRRRRRR$h'vLhhhvLLh LLPhPLL @;H=r"P0.hL4hhhhhhhvv hhhhhhh```$ ```$ ```LLLLLL Algebra: Average Word Problems  There are three main types of average problems commonly encountered in school algebra:  HYPERLINK "http://www.onlinemathlearning.com/average-problems.html" \l "mean#mean" Average (Arithmetic Mean),  HYPERLINK "http://www.onlinemathlearning.com/average-problems.html" \l "weighted-average#weighted-average" Weighted Average and  HYPERLINK "http://www.onlinemathlearning.com/average-problems.html" \l "average-speed#average-speed" Average Speed. Average (Arithmetic Mean) The average (arithmetic mean) uses the formula:  INCLUDEPICTURE "http://www.onlinemathlearning.com/image-files/average-problem-mean-formula-1.gif" \* MERGEFORMATINET  The formula can also be written as  INCLUDEPICTURE "http://www.onlinemathlearning.com/image-files/average-problem-mean-formula-2.gif" \* MERGEFORMATINET   Example: The average (arithmetic mean) of a list of 6 numbers is 20. If we remove one of the numbers, the average of the remaining numbers is 15. What is the number that was removed? Solution: Step 1: The removed number could be obtained by difference between the sum of original 6 numbers and the sum of remaining 5 numbers i.e. sum of original 6 numbers sum of remaining 5 numbers Step 2: Using the formula  INCLUDEPICTURE "http://www.onlinemathlearning.com/image-files/average-problem-mean-formula-2.gif" \* MERGEFORMATINET  sum of original 6 numbers = 20 6 = 120 sum of remaining 5 numbers = 15 5 = 75 Step 3: Using the formula from step 1 Number removed = sum of original 6 numbers sum of remaining 5 numbers 120 75 = 45 Answer: The number removed is 45.  Weighted Average Another type of average problem involves the weighted average - which is the average of two or more terms that do not all have the same number of members. To find the weighted term, multiply each term by its weighting factor, which is the number of times each term occurs. The formula for weighted average is:  INCLUDEPICTURE "http://www.onlinemathlearning.com/image-files/average-problem-weighted-formula-1.gif" \* MERGEFORMATINET  Example: A class of 25 students took a science test. 10 students had an average (arithmetic mean) score of 80. The other students had an average score of 60. What is the average score of the whole class? Solution: Step 1: To get the sum of weighted terms, multiply each average by the number of students that had that average and then sum them up. 80 10 + 60 15 = 800 + 900 = 1700 Step 2: Total number of terms = Total number of students = 25 Step 3: Using the formula  INCLUDEPICTURE "http://www.onlinemathlearning.com/image-files/average-problem-weighted-example-1.gif" \* MERGEFORMATINET  Answer: The average score of the whole class is 68. Be careful! You will get the wrong answer if you add the two average scores and divide the answer by two.  Average Speed Computation of average speed is a trickier type of average problems. Average speed uses the formula:  INCLUDEPICTURE "http://www.onlinemathlearning.com/image-files/average-problem-ave-speed-formula-1.gif" \* MERGEFORMATINET  Example: John drove for 3 hours at a rate of 50 miles per hour and for 2 hours at 60 miles per hour. What was his average speed for the whole journey? Solution: Step 1: The formula for distance is Distance = Rate Time Total distance = 50 3 + 60 2 = 270 Step 2: Total time = 3 + 2 = 5 Step 3: Using the formula  INCLUDEPICTURE "http://www.onlinemathlearning.com/image-files/average-problem-ave-speed-formula-1.gif" \* MERGEFORMATINET   INCLUDEPICTURE "http://www.onlinemathlearning.com/image-files/average-problem-270on5-1.gif" \* MERGEFORMATINET  Answer: The average speed is 54 miles per hour. Be careful! You will get the wrong answer if you add the two speeds and divide the answer by two. !"#|}[ \ l m r s 4 5 I J K L O P Q S [    h i j k l , hY3/0Jj'hY3/U hY3/0JhY3/0JB* phhY3/0J6B* ]phjhY3/UjhY3/Uj hY3/UjhY3/U hY3/0JjchY3/UjhY3/UhY3/=!%  4 M O S ]  -<^`dugdY3/gdY3/gdY3/gdY3/,<C`ab'()*+3 &'($%#*ڳڏŭ hY3/0Jj:3hY3/Uj0hY3/Uj2-hY3/U hY3/0J hY3/0Jj%hY3/UhY3/0JB* phhY3/0J6B* ]phjhY3/UjhY3/UjhY3/UjhY3/UhY3/0JB* phhY3/6+5$&*8'#B\QgdY3/gdY3/gdY3/*BI\]MNOPQY hY3/0J hY3/0Jj<hY3/Uj8hY3/UjhY3/UhY3/0JB* phhY3/,1h/ =!"#$% cDd,  c :ANormalFax01C"@0<!-- google_ad_client = "pub-9460199170054827"; /* algebra 468x60 */ google_ad_slot = "7930928586"; google_ad_width = 468; google_ad_height = 60; //--> type="text/javascript"b!X󆡑NBD nX󆡑NBPNG  IHDRfsRGB@}0PLTE{bIDATE!0Eq^uM&VUp\ &C|)"3.8̴(6 jPtsʄ&)NU- \^w& ^eyƾ_c|_^9IENDB`Dd,0  c :ANormalFax01C"ì src="http://pagead2.googlesyndication.com/pagead/show_ads.js" type="text/javascript"b!X󆡑NB nX󆡑NBPNG  IHDRfsRGB@}0PLTE{bIDATE!0Eq^uM&VUp\ &C|)"3.8̴(6 jPtsʄ&)NU- \^w& ^eyƾ_c|_^9IENDB`Dd1   S vA>average-problem-mean-formula-1mean formulab%ǐG5v}Q)L n%ǐG5v}Q)PNG  IHDR-ȚJ|tEXtSoftwareMicrosoft Office5q`PLTE tRNS@f pHYs@@bCc[ cmPPJCmp0712HsIDAThCXۖ00Emnm(I.ɲյyU]7TBq㮆7T%~!k8A.(afp`~cDHnJAC\FA? O! _.Ab: u"&׹UC!=7×O`bjT@q9 GS=|CTO؂/2@42zxi:Qz?#w 4 s2 ZPk0Ņ:~՛VgPCUȚ1"w!VPFs@?{e@m-g IdvV,)qC*ݙ#uɶCo i82#sż;˯_[o45{DzU@>Lu QǹK8Q] tS{aVFrzq86>̶ctăÔ!^PaDVKTq!~BOg)9^S#8X-Fαf~R}`]n*4g)P%JG/RQ!آP*d#u!0W/ZXB#{ IENDB`hDd;  S zA>average-problem-mean-formula-2mean formula 2bvZ:6i+^0R nJZ:6i+^0PNG  IHDR ѝtEXtSoftwareMicrosoft Office5q`PLTE tRNS@f pHYs@@bCc[ cmPPJCmp0712Hs5IDATXGWѶ )MA;w;JK-|M+l}ն_W9[ƲE]þW{GIe55pԄ|3{ڐZ <'{Ø@TBux Z,pS) h>zckLHVrd!G]/lklO`qȐ\G»Mc0%`/q`,L¶ W?Rܧ9J%E'o.L'eP˄dj!!*0XO-yYZ?lTU8-*=#?{c()bf9s> SzqPX= t,:Ijp` \R8iR QG ݢlAN'oL6'5Ƶ@ڟs8"?8yѹds$*&f)8 ;IeFjǤK Rv`6D'Z74pC2_ N{aGR76 L>ViMIENDB`cDd,  c :ANormalFax01C"@0<!-- google_ad_client = "pub-9460199170054827"; /* algebra 468x15 */ google_ad_slot = "5995971510"; google_ad_width = 468; google_ad_height = 15; //--> type="text/javascript"b!X󆡑NBc nX󆡑NBPNG  IHDRfsRGB@}0PLTE{bIDATE!0Eq^uM&VUp\ &C|)"3.8̴(6 jPtsʄ&)NU- \^w& ^eyƾ_c|_^9IENDB`Dd,0  c :ANormalFax01C"ì src="http://pagead2.googlesyndication.com/pagead/show_ads.js" type="text/javascript"b!X󆡑NB nX󆡑NBPNG  IHDRfsRGB@}0PLTE{bIDATE!0Eq^uM&VUp\ &C|)"3.8̴(6 jPtsʄ&)NU- \^w& ^eyƾ_c|_^9IENDB`hDd;  S zA>average-problem-mean-formula-2mean formula 2bvZ:6i+^0Rk nJZ:6i+^0PNG  IHDR ѝtEXtSoftwareMicrosoft Office5q`PLTE tRNS@f pHYs@@bCc[ cmPPJCmp0712Hs5IDATXGWѶ )MA;w;JK-|M+l}ն_W9[ƲE]þW{GIe55pԄ|3{ڐZ <'{Ø@TBux Z,pS) h>zckLHVrd!G]/lklO`qȐ\G»Mc0%`/q`,L¶ W?Rܧ9J%E'o.L'eP˄dj!!*0XO-yYZ?lTU8-*=#?{c()bf9s> SzqPX= t,:Ijp` \R8iR QG ݢlAN'oL6'5Ƶ@ڟs8"?8yѹds$*&f)8 ;IeFjǤK Rv`6D'Z74pC2_ N{aGR76 L>ViMIENDB`cDd,  c :ANormalFax01C"@0<!-- google_ad_client = "pub-9460199170054827"; /* algebra 468x15 */ google_ad_slot = "5995971510"; google_ad_width = 468; google_ad_height = 15; //--> type="text/javascript"b!X󆡑NB nX󆡑NBPNG  IHDRfsRGB@}0PLTE{bIDATE!0Eq^uM&VUp\ &C|)"3.8̴(6 jPtsʄ&)NU- \^w& ^eyƾ_c|_^9IENDB`Dd,0   c :ANormalFax01C"ì src="http://pagead2.googlesyndication.com/pagead/show_ads.js" type="text/javascript"b!X󆡑NB6 nX󆡑NBPNG  IHDRfsRGB@}0PLTE{bIDATE!0Eq^uM&VUp\ &C|)"3.8̴(6 jPtsʄ&)NU- \^w& ^eyƾ_c|_^9IENDB`!Dd   S AF*average-problem-weighted-formula-1weighted ave formula b}v 㜔 0s n}v 㜔 0sPNG  IHDR -9FtEXtSoftwareMicrosoft Office5q`PLTE tRNS@f pHYs@@bCc[ cmPPJCmp0712HsIDAThCY 0 _z!dãfigc4ʲnBBBBvm$>3f7nCHFM8|)t g-'zEO!( *,W[l=T`$A5bPdZe`LS3>=NyDa[LIb%GŜ@rsxH`?1 06keCji;0.S|rhhcd8e-gCЎmnט z$p>nBճO"/[_klڥ0mC{; ڃl3 "] MK>!#yddTP\bzyd,z{:T^W)HV :\{>c3!:r'x/U 91s,"LO B):F^ 9]]K&Fx= 'ӷ஠3!VЂڬЉ1m0IBaTwCѮ?Zl)D4`$IΏ'R&n9ej`DP`3e; [9%EÒrj<./ W-C}H{8-^4 5a |P 5kq^Ƨ;eifA,Bϵq,e)%-]fGh!T beR-zK.Gw#L.JH 'bn`gqbܟ>Y2S(\>|5Z6ʑOSSܥ5/IHtg|ߵD1GK~B/s s'9:ZKC7&=fZXVrq9҃*ڊˠ4 ,r/vQI)m9.wes{g;#w+$&O+(d>D g>b' V^56Sa"+ ҝ40>5AMhb?0~t #1a~wv?{}@mfr43AoiFr\5b@π(|?i~hCMLLL.&Fuy ~8߻5Fy|>x;۵;@ S +h]MP;*'m@GY/B&(#~LC? ¦IENDB`cDd,   c :ANormalFax01C"@0<!-- google_ad_client = "pub-9460199170054827"; /* algebra 468x15 */ google_ad_slot = "5995971510"; google_ad_width = 468; google_ad_height = 15; //--> type="text/javascript" b!X󆡑NBv- nX󆡑NBPNG  IHDRfsRGB@}0PLTE{bIDATE!0Eq^uM&VUp\ &C|)"3.8̴(6 jPtsʄ&)NU- \^w& ^eyƾ_c|_^9IENDB`Dd,0   c :ANormalFax01C"ì src="http://pagead2.googlesyndication.com/pagead/show_ads.js" type="text/javascript" b!X󆡑NB0 nX󆡑NBPNG  IHDRfsRGB@}0PLTE{bIDATE!0Eq^uM&VUp\ &C|)"3.8̴(6 jPtsʄ&)NU- \^w& ^eyƾ_c|_^9IENDB`Dd]   S AH,average-problem-ave-speed-formula-1average speed formula bF T$3 N~3 nF T$3 NPNG  IHDR-AtEXtSoftwareMicrosoft Office5q`PLTE tRNS@f pHYs@@bCc[ cmPPJCmp0712HsIDAThCXr k-X6Ф# ;zH%z|q|59*phB^`B Y3/ Normal (Web)dd[$\$6o6 Y3/normaldd[$\$Jo!J Y3/highlight-example1CJaJph.X`1. Y3/Emphasis6]*W`A* Y3/Strong5\DoQD Y3/highlight-step1CJaJphJoaJ Y3/highlight-caution1CJaJph3$!%4MOS] -<^`du+5  $ & * 8  ' # B \ Q@00000@0@0@0@0@00000@0@0@0@0@00 0 0 0 0 0 0 0 @0@000@0@0@00@0@000000@0@000@0@0@00 @0@00#0!%4MOS] -<^`du+5  $ & * 8  ' # B \ Q00000@0@0@0000@0@0 @0 0 0 0 0 0 0 @0@00@0000@0000@0@00@0@00 @0 0 0,*  |[lr4IKhj')   \ MOXXXCCCCCCCCmeanweighted-average average-speedd* d* lo33MS  }  N,Ntdd0m ,NtddoD4O,Ntdd-0b,Ntdde=n,Ntddpso,NtddrR]q,Ntdd,Nt`du,Ntddx,Ntdd-uu|,NtddY3/@ P@UnknownGz Times New Roman5Symbol3& z Arial7&  Verdana"hsنtن8 8 !242HX)?Y3/Algebra: Average Word Problems Lynn Speegle Lynn SpeegleOh+'0  $0 P \ ht| Algebra: Average Word ProblemsLynn SpeegleNormalLynn Speegle1Microsoft Office Word@F#@?G=@HH=8 ՜.+,D՜.+,` hp  Oxford School District' Algebra: Average Word Problems Title 8@ _PID_HLINKSAt R8http://www.onlinemathlearning.com/average-problems.htmlaverage-speed#average-speeda>8http://www.onlinemathlearning.com/average-problems.html"weighted-average#weighted-average"v8http://www.onlinemathlearning.com/average-problems.html mean#mean  !"#$%&'()*+,-./012456789:;<=>?@BCDEFGHJKLMNOPSRoot Entry F0Ϫ;H=UData ?1Table3WordDocument.$SummaryInformation(ADocumentSummaryInformation8ICompObjq  FMicrosoft Office Word Document MSWordDocWord.Document.89q