小学六年级奥数浓度问题 六年级奥数浓度问题
\u4e00\u9053\u516d\u5e74\u7ea7\u5965\u6570\u9898 \u5173\u4e8e\u6d53\u5ea6\u95ee\u9898\u5f53\u7b2c\u4e8c\u6b21\u4ece\u4e59\u5bb9\u5668\u5f80\u7532\u5bb9\u5668\u5012\u4e00\u90e8\u5206\u6df7\u5408\u6db2\u540e\uff0c\u4e59\u5bb9\u5668\u4e2d\u5269\u4e0b\u7684\u6df7\u5408\u6db2\u9152\u7cbe\u536025\uff05\uff0c\u90a3\u4e48\u7b2c\u4e8c\u6b21\u8fd8\u6ca1\u5012\u65f6\uff0c\u4e59\u5bb9\u5668\u4e2d\u7684\u6df7\u5408\u6db2\u4e2d\u9152\u7cbe\u4e59\u536025\uff05\uff0c\u6c34\u536075\uff05\uff0c\u7b2c\u4e00\u6b21\u4ece\u7532\u5bb9\u5668\u5012\u5165\u4e59\u5bb9\u5668\u7684\u662f\u7eaf\u9152\u7cbe\uff0c\u6240\u4ee5\u8fd9\u65f6\u4e59\u5bb9\u5668\u4e2d\u7684\u6c34\u8fd8\u662f15\u5347\uff0c\u4e59\u5bb9\u5668\u4e2d\u7684\u6df7\u5408\u6db2\u5c31\u662f15\u00f775\uff05\uff1d20\u5347\uff0c\u5373\u7b2c\u4e00\u6b21\u5012\u5165\u4e59\u5bb9\u5668\u7684\u7eaf\u9152\u7cbe\u662f20-15\uff1d5\u5347\uff0c\u7532\u5bb9\u5668\u4e2d\u73b0\u5728\u8fd8\u5269\u7eaf\u9152\u7cbe11-5\uff1d6\u5347\uff0c\u7b2c\u4e8c\u6b21\u4ece\u4e59\u5012\u5165\u7532\u7684\u6df7\u5408\u6db2\u536025\uff05\uff0c\u6240\u4ee5\u6c34\u536075\uff05\uff1d\u56db\u5206\u4e4b\u4e09\uff0c\u800c\u8fd9\u4e9b\u6c34\u5012\u5165\u7532\u5bb9\u5668\u4e2d\u53ea\u5360\u6df7\u5408\u6db2\u76841-62.5\uff05\uff1d\u516b\u5206\u4e4b\u4e09\uff0c\u8bf4\u660e\u4ece\u4e59\u5bb9\u5668\u5012\u5165\u7532\u7684\u6df7\u5408\u6db2\u4f7f\u7532\u4e2d\u7684\u603b\u6570\u91cf\u589e\u52a0\u4e86\u4e00\u500d\uff0c\u6240\u4ee5\u7b2c\u4e8c\u6b21\u4ece\u4e59\u5bb9\u5668\u5012\u5165\u7532\u7684\u6df7\u5408\u6db2\u662f6\u5347\uff0e
\u516d\u5e74\u7ea7\u4e13\u9898\u8bb2\u5ea7\uff08\u4e8c\u5341\u4e09\uff09
\u6d53\u5ea6\u95ee\u9898 \u8d75\u4e39
\u57fa\u7840\u77e5\u8bc6
\u6eb6\u6db2\u7684\u91cd\u91cf=\u6eb6\u8d28\u7684\u91cd\u91cf+\u6eb6\u5242\u7684\u91cd\u91cf \u6d53\u5ea6=\u6eb6\u8d28\u91cd\u91cf\u00f7\u6eb6\u6db2\u91cd\u91cf
\u6eb6\u6db2\u91cd\u91cf=\u6eb6\u8d28\u91cd\u91cf\u00f7\u6d53\u5ea6 \u6eb6\u8d28\u91cd\u91cf=\u6eb6\u6db2\u91cd\u91cf\u00d7\u6d53\u5ea6
\u4e24\u79cd\u6d53\u5ea6\u4e0d\u540c\u7684\u6eb6\u6db2\uff0c\u8bbe\uff1a\u7532\u7684\u6d53\u5ea6\u4e3aa\uff0c\u6eb6\u6db2\u7684\u91cd\u91cf\u4e3aA\uff1b\u4e59\u7684\u6d53\u5ea6\u4e3ab\uff0c\u6eb6\u6db2\u91cd\u91cfB\uff0c\u6df7\u5408\u540e\u6d53\u5ea6\u4e3ac\u3002\u4e14a\uff1eb\uff0c\u5219\u6709
\u4f8b1 \u4e00\u5bb9\u5668\u5185\u6709\u6d53\u5ea6\u4e3a25\uff05\u7684\u7cd6\u6c34\uff0c\u82e5\u518d\u52a0\u516520\u5343\u514b\u6c34\uff0c\u5219\u7cd6\u6c34\u7684\u6d53\u5ea6\u53d8\u4e3a15\uff05\uff0c\u95ee\u8fd9\u4e2a\u5bb9\u5668\u5185\u539f\u6765\u542b\u6709\u7cd6\u591a\u5c11\u5343\u514b\uff1f
\u89e3\uff1a\u8bbe\u6d53\u5ea6\u4e3a25\uff05\u7684\u7cd6\u6c34\u539f\u6765\u91cd\u91cf\u4e3ax\uff0c\u5217\u65b9\u7a0b
\uff0c\u89e3\u5f97 x=30\uff0c\u5219\u8fd9\u4e2a\u5bb9\u5668\u5185\u539f\u6765\u542b\u6709\u7cd6\uff1a30\u00d70\u300225=7.5 \u5343\u514b
\u4f8b2 \u7532\u3001\u4e59\u4e24\u53ea\u88c5\u6ee1\u786b\u9178\u6eb6\u6db2\u7684\u5bb9\u5668\uff0c\u7532\u5bb9\u5668\u4e2d\u88c5\u6709\u6d53\u5ea6\u4e3a8\uff05\u7684\u786b\u9178\u6eb6\u6db2600\u5343\u514b\uff0c\u4e59\u5bb9\u5668\u4e2d\u88c5\u6709\u6d53\u5ea6\u4e3a40\uff05\u7684\u786b\u9178\u6eb6\u6db2400\u5343\u514b.\u5404\u53d6\u591a\u5c11\u5343\u514b\u5206\u522b\u653e\u5165\u5bf9\u65b9\u5bb9\u5668\u4e2d\uff0c\u624d\u80fd\u4f7f\u8fd9\u4e24\u4e2a\u5bb9\u5668\u4e2d\u7684\u786b\u9178\u6eb6\u6db2\u7684\u6d53\u5ea6\u4e00\u6837\uff1f
\u89e3\uff1a\u8bbe\u5404\u53d6 x\u5343\u514b\u5206\u522b\u653e\u5165\u5bf9\u65b9\u5bb9\u5668\u4e2d\uff0c\u5217\u65b9\u7a0b
\uff0c\u89e3\u5f97x=240\uff08\u5343\u514b\uff09
\u4f8b3 \u73b0\u6709\u6d53\u5ea6\u4e3a10\uff05\u7684\u76d0\u6c3420\u5343\u514b\uff0c\u518d\u52a0\u5165\u591a\u5c11\u5343\u514b\u6d53\u5ea6\u4e3a30\uff05\u7684\u76d0\u6c34\uff0c\u53ef\u4ee5\u5f97\u5230\u6d53\u5ea6\u4e3a22\uff05\u7684\u76d0\u6c34\uff1f
\u89e3\uff1a\u8bbe\u518d\u52a0\u5165\u6d53\u5ea6\u4e3a30\uff05\u7684\u76d0\u6c34x\u5343\u514b\uff0c\u5217\u65b9\u7a0b
0.22\uff0c\u89e3\u5f97x=30\uff08\u5343\u514b\uff09
\u4f8b4 \u73b0\u6709\u6d53\u5ea6\u4e3a10\uff05\u7684\u76d0\u6c348\u5343\u514b\uff0c\u8981\u5f97\u5230\u6d53\u5ea6\u4e3a20\uff05\u7684\u76d0\u6c34\uff0c\u7528\u4ec0\u4e48\u65b9\u6cd5\u53ef\u4ee5\u5f97\u5230\uff0c\u5177\u4f53\u5982\u4f55\u64cd\u4f5c\uff1f
\u89e3\uff1a\u65b9\u6cd5\uff081\uff09\u52a0\u76d0.\u8bbe\u52a0\u76d0x\u5343\u514b\uff0c\u52190.2 \u89e3\u5f97x=1\uff08\u5343\u514b\uff09
\u65b9\u6cd5\uff082\uff09\u84b8\u53d1\u6c34.\u8bbe\u84b8\u53d1\u6c34x\u5343\u514b\uff0c\u5219=0.2 \u89e3\u5f97x=4\uff08\u5343\u514b\uff09
\u4f8b5 \u5728\u6d53\u5ea6\u4e3a40\uff05\u7684\u9152\u7cbe\u6eb6\u6db2\u4e2d\u52a0\u51655\u5343\u514b\u6c34\uff0c\u6d53\u5ea6\u53d8\u4e3a30\uff05\uff0c\u518d\u52a0\u5165\u591a\u5c11\u5343\u514b\u9152\u7cbe\uff0c\u6d53\u5ea6\u53d8\u4e3a50\uff05\uff1f
\u89e3\uff1a\u8bbe\u6d53\u5ea6\u4e3a40\uff05\u7684\u9152\u7cbe\u6eb6\u6db2\u6709x\u5343\u514b\uff0c\u7531\u4e0a\u9762\u7684\u516c\u5f0f\uff0c
\u6709= \u89e3\u5f97x=15\uff08\u5343\u514b\uff09\uff0c\u5219\u6d53\u5ea6\u53d8\u4e3a30\uff05\u7684\u9152\u7cbe\u6eb6\u6db2\u670920\u5343\u514b.
\u8bbe\u518d\u52a0\u5165 y\u5343\u514b\u9152\u7cbe\u6d53\u5ea6\u53d8\u4e3a50\uff05\u3002\u5219=0.5\uff0c\u89e3\u5f97y=8\uff08\u5343\u514b\uff09
\u4f8b6\u7532\u79cd\u9152\u7cbe\u7684\u7eaf\u9152\u7cbe\u542b\u91cf\u4e3a72%\uff0c\u4e59\u79cd\u9152\u7cbe\u7684\u7eaf\u9152\u7cbe\u542b\u91cf\u4e3a58%\uff0c\u6df7\u5408\u540e\u7eaf\u9152\u7cbe\u7684\u542b\u91cf\u4e3a62%\u3002\u5982\u679c\u6bcf\u79cd\u9152\u7cbe\u53d6\u7684\u6570\u91cf\u90fd\u6bd4\u539f\u6765\u591a\u53d615\u5347\uff0c\u6df7\u5408\u540e\u7684\u9152\u7cbe\u542b\u91cf\u4e3a63.25%\uff0c\u95ee\u7b2c\u4e00\u6b21\u6df7\u5408\u65f6\uff0c\u7532\u3001\u4e59\u4e24\u79cd\u9152\u7cbe\u5404\u53d6\u591a\u5c11\u5347\uff1f
\u89e3\uff1a\u8bbe\u7532\u79cd\u9152\u7cbe\u7684\u91cf\u4e3aA\uff0c\u4e59\u79cd\u9152\u7cbe\u7684\u91cf\u4e3aB\uff0c\u7531\u7b2c\u4e00\u6b21\u6df7\u5408\u540e\u7eaf\u9152\u7cbe\u7684\u542b\u91cf\u4e3a62%\u3002
\u5219\u6709 = \u6240\u4ee5=.\u518d\u8bbe\u7532\u79cd\u9152\u7cbe\u7684\u91cf\u4e3a2x\uff0c\u4e59\u79cd\u9152\u7cbe\u7684\u91cf5 x
\u6bcf\u79cd\u9152\u7cbe\u53d6\u7684\u6570\u91cf\u90fd\u6bd4\u539f\u6765\u591a\u53d615\u5347\uff0c\u518d\u6df7\u5408\u540e\uff0c\u7531\u4e0a\u9762\u7684\u516c\u5f0f\uff0c
\u5219\u6709 =\uff0c\u6240\u4ee5=
\u89e3\u51fax=6\u3002\u7532\u79cd\u9152\u7cbe\u53d612\u5347\uff0c\u4e59\u79cd\u9152\u7cbe\u53d630\u5347
\u7ec3\u4e60\u4e94
1. \u73b0\u6709\u6d53\u5ea6\u4e3a20\uff05\u7684\u7cd6\u6c3420\u5343\u514b\uff0c\u8981\u5f97\u5230\u6d53\u5ea6\u4e3a10\uff05\u7684\u7cd6\u6c34\uff0c\u9700\u52a0\u6c34\u591a\u5c11\u5343\u514b\uff1f
2. \u8981\u914d\u5236\u6d53\u5ea6\u4e3a20\uff05\u7684\u76d0\u6c341000\u514b\uff0c\u9700\u6d53\u5ea6\u4e3a10\uff05\u548c\u6d53\u5ea6\u4e3a30\uff05\u7684\u76d0\u6c34\u5404\u591a\u5c11\u514b\uff1f
3. \u4e00\u5bb9\u5668\u5185\u88c5\u670910\u5347\u7eaf\u9152\u7cbe\uff0c\u5012\u51fa2.5\u5347\u540e\uff0c\u7528\u6c34\u52a0\u6ee1\uff0c\u518d\u5012\u51fa5\u5347\uff0c\u518d\u7528\u6c34\u52a0\u6ee1\uff0c\u8fd9\u65f6\u5bb9\u5668\u5185\u7684\u6eb6\u6db2\u7684\u6d53\u5ea6\u662f\u591a\u5c11\uff1f
4. \u5728\u6d53\u5ea6\u4e3a20\uff05\u7684\u76d0\u6c34\u4e2d\u52a0\u516510\u5343\u514b\u6c34\uff0c\u6d53\u5ea6\u53d8\u4e3a15\uff05\uff0c\u518d\u52a0\u5165\u591a\u5c11\u5343\u514b\u76d0\uff0c\u6d53\u5ea6\u53d8\u4e3a25\uff05\uff1f\uff05
5. \u7532\u79cd\u9152\u7cbe\u6eb6\u6db2\u4e2d\u6709\u9152\u7cbe6\u5347\uff0c\u6c349\u5347\uff1b\u4e59\u79cd\u9152\u7cbe\u6eb6\u6db2\u4e2d\u6709\u9152\u7cbe9\u5347\uff0c\u6c343\u5347\uff1b\u8981\u914d\u5236\u621050\uff05\u7684\u9152\u7cbe\u6eb6\u6db27\u5347\uff0c\u95ee\u4e24\u79cd\u9152\u7cbe\u6eb6\u6db2\u5404\u9700\u591a\u5c11\u5347\uff1f
6\u3001\u6d53\u5ea6\u4e3a20%\u300118%\u300116%\u7684\u4e09\u79cd\u76d0\u6c34\uff0c\u6df7\u5408\u540e\u5f97\u5230100\u514b18.8%\u7684\u76d0\u6c34\uff0c\u5982\u679c18%\u7684\u76d0\u6c34\u6bd416%\u7684\u76d0\u6c34\u591a30\u514b\uff0c\u95ee\u6bcf\u79cd\u76d0\u6c34\u5404\u591a\u5c11\u514b\uff1f
da
1\u300120\u5343\u514b
2\u3001\u5404500\u5343\u514b\uff0c
3\u300137\uff0e5\uff05
4\u3001\u5343\u514b
5\u3001\u7532\u79cd\u9152\u7cbe\u6eb6\u6db25 \u5347\uff1b\u4e59\u79cd\u9152\u7cbe\u6eb6\u6db22\u5347\u3002
6\u3001\u8bbe\u6d53\u5ea6\u4e3a16%\u7684\u76d0\u6c34x\u514b\uff0c\u6d53\u5ea6\u4e3a18%\u7684\u76d0\u6c34\uff08x+30\uff09\u514b\uff0c\u6d53\u5ea6\u4e3a20%\u76d0\u6c34\u4e3a100-\uff082 x+30\uff09=\uff0870-2 x\uff09\u514b\u3002\u5217\u65b9\u7a0b\uff1a0.2 \u00d7\uff0870-2 x\uff09+0.18 \u00d7\uff08x+30\uff09+0.16 x=18.8 \u89e3\u5f97x=10\u514b
解：设需要浓度为25%的乙溶液x克
100 ×15%+25%x = （100+x）20%
x=100
答：需要浓度为25%的乙溶液100克
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绛旓細瑙ｏ細璁惧彇娴撳害45%绯栨按x鍏嬶紝鍒欏彇娴撳害5%鐨勭硸姘达紙400-x锛夊厠銆45%x+5%*(400-x)=400*30 40%x+20=120 x=250 400-250=150锛堝厠锛夌瓟锛氭祿搴45%绯栨按250鍏嬶紝娴撳害5%绯栨按150鍏嬨
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绛旓細鍋囪16%鐨勭洂姘磝鍏嬶紝30%鐨勭洂姘磞鍏嬶紝娣峰悎鍚庯細婧舵恫鎬昏川閲忎笉鍙橈細x+y=350 婧惰川鐨勬昏川閲忎笉鍙橈細0.16x+0.3y=0.24*350 鑱旂珛瑙ｅ緱x=150鍏嬨傚浜150鍏嬬殑16%鐩愭按锛氬亣璁10%鐨勭洂姘碼鍏嬶紝20%鐨勭洂姘碽鍏嬶紝娣峰悎鍚庯細婧舵恫鎬昏川閲忎笉鍙橈細a+b=150 婧惰川鐨勬昏川閲忎笉鍙橈細0.1a+0.2b=0.16*150 鑱旂珛瑙ｅ緱a=60鍏,...
绛旓細绛旓細鐢40鍗冨厠鐨娴撳害涓35锛呯殑鍐滆嵂涓坊鍔760鍗冨厠姘达紝鎵嶈兘閰嶆垚娴撳害涓1.75锛呯殑鍐滆嵂800鍗冨厠銆備緥棰3銆傜幇鏈夋祿搴︿负10锛呯殑鐩愭按20鍗冨厠銆傚啀鍔犲叆澶氬皯鍗冨厠娴撳害涓30锛呯殑鐩愭按锛屽彲浠ュ緱鍒版祿搴︿负22锛呯殑鐩愭按锛熴愭濊矾瀵艰埅銆戣繖鏄竴涓憾娑叉贩鍚闂銆傛贩鍚堝墠銆佸悗婧舵恫鐨勬祿搴︽敼鍙樹簡锛屼絾鎬讳綋涓婃憾璐ㄥ強婧舵恫鐨勬昏川閲忔病鏈夋敼鍙樸傛墍浠ワ紝...
绛旓細鈥滄暟鐞嗙瓟鐤戝洟鈥濅负鎮ㄨВ绛旓紝甯屾湜瀵逛綘鏈夋墍甯姪銆傝В锛氳闇瑕娴撳害涓25%鐨勪箼婧舵恫x鍏 100 脳15%+25%x = 锛100+x锛20 x=100 绛旓細闇瑕佹祿搴︿负25%鐨勪箼婧舵恫100鍏 濡傛灉浣犺鍙垜鐨勫洖绛旓紝鏁鍙婃椂閲囩撼锛寏濡傛灉浣犺鍙垜鐨勫洖绛旓紝璇峰強鏃剁偣鍑汇愰噰绾充负婊℃剰鍥炵瓟銆戞寜閽 ~~鎵嬫満鎻愰棶鐨勬湅鍙嬪湪瀹㈡埛绔彸涓婅璇勪环鐐广...
绛旓細1.鐜版湁鍚洂鐧惧垎涔嬩笁鍗佺殑鐩愭按120鍏嬶紝瑕佷娇鏂扮殑鐩愭按鍙樹负鍚洂涓虹櫨鍒嗕箣鍥涘崄鐨勭洂姘达紝闇钂稿彂姘村灏戯紵鐩:120x30%=36鍏 姘达細120-36=84鍏 鐩愶細姘=36锛84=3锛7=6锛14 鐩愶細姘=40锛60=2锛3=6锛9 姣忎唤锛120/锛6+14锛=6锛堝厠锛夐渶钂稿彂姘达細6x(14-9)=30(鍏嬶級2.鍦娴撳害涓虹櫨鍒嗕箣涓夊崄鐨120鍏嬬硸姘...
绛旓細瑙ｏ細棣栧厛璁＄畻涓変釜鐡跺瓙娴撳害閮界浉绛夋椂鐨勬祿搴涓猴紝x=锛40%*60+60%*120+25%*180锛/锛60+120+180锛 =39.1667 杩欎釜棰樻棤瑙ｏ紝鍘熷洜鍦ㄤ簬锛岃浣垮緱鏈鍚庝笁涓澂瀛愭祿搴︾浉绛夛紝鏈鍚庢搷浣滅殑鏄澂瀛愪笝锛屾妸浠庝笝鐡朵腑鍙栧嚭鐨凚鍏嬮厭绮惧掑叆鐢茬摱锛孋鍏嬮厭绮惧掑叆涔欑摱銆備篃灏辨槸璇翠粠涓欑鍙栧嚭鍚庡墿浣欑殑婧舵恫娴撳害涓猴紝39.1667%锛...
绛旓細銆愮啛鑳界敓宸с戯紙姣忛10鍒嗭級1銆 鐜板湪鏈娴撳害涓20锛呯殑绯栨按300鍏嬶紝瑕佹妸瀹冨彉鎴愭祿搴︿负40锛呯殑绯栨按锛岄渶瑕佸姞绯栧灏戝厠锛300脳锛1锛20锛咃級梅锛1锛40锛咃級锛300锛100鍏 2銆 鏈夊惈鐩15锛呯殑鐩愭按20鍗冨厠锛岃浣跨洂姘寸殑娴撳害涓20锛咃紝闇鍔犵洂澶氬皯鍗冨厠锛 20脳锛1锛15锛咃級梅锛1锛20锛咃級锛20锛1.25鍗冨厠 3銆 ...
绛旓細灏忓濂ユ暟鍚э紵鐢娴撳害涓夎銆傘傘傝繖鏍疯鍚ф妸娣峰悎鐨勪袱绉嶇墿璐ㄥ苟鎺掑啓鍦ㄤ竴寮犵焊涓婏紝鎶婁粬浠殑娴撳害鍜岃川閲忓啓鍦ㄤ粬浠梺杈癸紝鎶婃贩鍚堝悗鐨勭墿璐ㄥ啓鍦ㄩ偅涓や釜鐗╄川鐨勪腑闂寸殑涓嬫柟锛岃繖鏍蜂笁绉嶇墿璐ㄥ舰鎴愪簡涓涓掍笁瑙掑舰銆傛瘮濡傝杩涜娣峰悎鐨勪袱鐗╄川鏄疉鍜孊锛屾祿搴﹀垎鍒槸m鍜宯锛岃川閲忓垎鍒槸x鍜寉锛屾贩鍚堝悗鐨勭墿璐ㄦ槸C锛屾祿搴︽槸p锛岃川閲忔槸z銆
绛旓細1.娴撳害涓鑸互璐ㄩ噺娴撳害璁＄畻锛屽師鏉ョ殑鐩愭按娴撳害涓20鍏嬬洂姣斾笂锛20鍏嬬洂鍔80鍏嬫按锛夈20/锛20+80锛=0.2 鍚庢潵鐨勭洂姘翠腑鐩愯川閲忔病鏈夊彉锛岃捀鍙戠殑鏄按鐨勮川閲忥紝鍥犳娴撳害搴旇涓20/锛20+50锛=0.28574 鎵浠ユ祿搴︽瘮鍘熸潵鐨勬彁楂0.28574-0.2=0.08574=0.086=8.6 2.鐢茬閰掔簿6鍗囷紝姘9鍗 閰嶇疆鎴愮殑閰掔簿鍚噺40 ...
