小学奥数分类—浓度问题

\u5c0f\u5b66\u5965\u6570\u6d53\u5ea6\u95ee\u9898\u6709\u5173\u4f8b\u9898

\u3010\u719f\u80fd\u751f\u5de7\u3011\uff08\u6bcf\u989810\u5206\uff09
1\u3001 \u73b0\u5728\u6709\u6d53\u5ea6\u4e3a20\uff05\u7684\u7cd6\u6c34300\u514b\uff0c\u8981\u628a\u5b83\u53d8\u6210\u6d53\u5ea6\u4e3a40\uff05\u7684\u7cd6\u6c34\uff0c\u9700\u8981\u52a0\u7cd6\u591a\u5c11\u514b\uff1f
300\u00d7\uff081\uff0d20\uff05\uff09\u00f7\uff081\uff0d40\uff05\uff09\uff0d300\uff1d100\u514b
2\u3001 \u6709\u542b\u76d015\uff05\u7684\u76d0\u6c3420\u5343\u514b\uff0c\u8981\u4f7f\u76d0\u6c34\u7684\u6d53\u5ea6\u4e3a20\uff05\uff0c\u9700\u52a0\u76d0\u591a\u5c11\u5343\u514b\uff1f 20\u00d7\uff081\uff0d15\uff05\uff09\u00f7\uff081\uff0d20\uff05\uff09\uff0d20\uff1d1.25\u5343\u514b
3\u3001 \u7528\u542b\u6c280.15\uff05\u7684\u6c28\u6c34\u8fdb\u884c\u6cb9\u83dc\u8ffd\u80a5\u3002\u73b0\u6709\u542b\u6c2816\uff05\u7684\u6c28\u6c3430\u5343\u514b\uff0c\u914d\u7f6e\u65f6\u9700\u52a0\u6c34\u591a\u5c11\u5343\u514b\uff1f 30\u00d7\uff0816\uff05\uff0d0.15\uff05\uff09\u00f70.15\uff05\uff1d3170\u5343\u514b
4\u3001 \u4ed3\u5e93\u8fd0\u6765\u542b\u6c34\u91cf\u4e3a90\uff05\u7684\u4e00\u79cd\u6c34\u679c100\u5343\u514b\u3002\u4e00\u661f\u671f\u540e\u518d\u6d4b\uff0c\u53d1\u73b0\u542b\u6c34\u91cf\u964d\u4f4e\u523080\uff05\u3002\u73b0\u5728\u8fd9\u6279\u6c34\u679c\u7684\u8d28\u91cf\u662f\u591a\u5c11\u5343\u514b\uff1f

100\u00d7\uff081\uff0d90\uff05\uff09\u00f7\uff081\uff0d80\uff05\uff09\uff1d50\u5343\u514b
5\u3001 \u5728100\u5343\u514b\u6d53\u5ea6\u4e3a50\uff05\u7684\u786b\u9178\u6eb6\u6db2\u4e2d\uff0c\u518d\u52a0\u5165\u591a\u5c11\u5343\u514b\u6d53\u5ea6\u4e3a5\uff05\u7684\u786b\u9178\u6eb6\u6db2\u5c31\u53ef\u4ee5\u914d\u5236\u621025\uff05\u7684\u786b\u9178\u6eb6\u6db2\uff1f

100\u00d7\uff0850\uff05\uff0d25\uff05\uff09\u00f7\uff0825\uff05\uff0d5\uff05\uff09\uff1d125\u5343\u514b 6\u3001 \u6d53\u5ea6\u4e3a70\uff05\u7684\u9152\u7cbe\u6eb6\u6db2500\u514b\u4e0e\u6d53\u5ea6\u4e3a50\uff05\u7684\u9152\u7cbe\u6eb6\u6db2300\u514b\u6df7\u5408\u540e\u6240\u5f97\u5230\u7684\u9152\u7cbe\u6eb6\u6db2\u7684\u6d53\u5ea6\u662f\u591a\u5c11\uff1f

\uff08500\u00d770\uff05+300\u00d750\uff05\uff09\u00f7\uff08500+300\uff09\u00d7100\uff05\uff1d62.5\uff05
7\u3001 \u4e24\u79cd\u94a2\u5206\u522b\u542b\u954d5\uff05\u548c40\uff05\uff0c\u8981\u5f97\u5230140\u5428\u542b\u954d30\uff05\u7684\u94a2\uff0c\u9700\u8981\u542b\u954d5\uff05\u7684\u94a2\u548c\u542b\u954d40\uff05\u7684\u94a2\u5404\u591a\u5c11\u5428\uff1f

\u89e3\uff1a\u8bbe\u9700\u542b\u954d5\uff05\u7684\u94a2x\u5428\uff0c\u5219\u542b\u954d40\uff05\u7684\u94a2140\uff0dx\u5428\uff0c 5\uff05x+\uff08140\uff0dx\uff09\u00d740\uff05\uff1d140\u00d730\uff05 X \uff1d40 140\uff0d40\uff1d100\u5428
8\u3001 \u7532\u3001\u4e59\u4e24\u79cd\u9152\u5404\u542b\u9152\u7cbe75\uff05\u548c55\uff05\uff0c\u8981\u914d\u5236\u542b\u9152\u7cbe65\uff05\u7684\u91523000\u514b\uff0c\u5e94\u5f53\u4ece\u8fd9\u4e24\u79cd\u9152\u4e2d\u5404\u53d6\u591a\u5c11\u514b\uff1f
\uff083000\u00d775\uff05\uff0d3000\u00d765\uff05\uff09\u00f7\u30101\u00d7\uff0875\uff05\uff0d55\uff05\uff09\u3011\uff1d1500\u514b 3000\uff0d1500\uff1d1500\u514b
\u3010\u719f\u80fd\u751f\u5de7\u3011\uff08\u6bcf\u989810\u5206\uff09
1\u3001 \u73b0\u5728\u6709\u6d53\u5ea6\u4e3a20\uff05\u7684\u7cd6\u6c34300\u514b\uff0c\u8981\u628a\u5b83\u53d8\u6210\u6d53\u5ea6\u4e3a40\uff05\u7684\u7cd6\u6c34\uff0c\u9700\u8981\u52a0\u7cd6\u591a\u5c11\u514b\uff1f
300\u00d7\uff081\uff0d20\uff05\uff09\u00f7\uff081\uff0d40\uff05\uff09\uff0d300\uff1d100\u514b
2\u3001 \u6709\u542b\u76d015\uff05\u7684\u76d0\u6c3420\u5343\u514b\uff0c\u8981\u4f7f\u76d0\u6c34\u7684\u6d53\u5ea6\u4e3a20\uff05\uff0c\u9700\u52a0\u76d0\u591a\u5c11\u5343\u514b\uff1f 20\u00d7\uff081\uff0d15\uff05\uff09\u00f7\uff081\uff0d20\uff05\uff09\uff0d20\uff1d1.25\u5343\u514b
3\u3001 \u7528\u542b\u6c280.15\uff05\u7684\u6c28\u6c34\u8fdb\u884c\u6cb9\u83dc\u8ffd\u80a5\u3002\u73b0\u6709\u542b\u6c2816\uff05\u7684\u6c28\u6c3430\u5343\u514b\uff0c\u914d\u7f6e\u65f6\u9700\u52a0\u6c34\u591a\u5c11\u5343\u514b\uff1f 30\u00d7\uff0816\uff05\uff0d0.15\uff05\uff09\u00f70.15\uff05\uff1d3170\u5343\u514b
4\u3001 \u4ed3\u5e93\u8fd0\u6765\u542b\u6c34\u91cf\u4e3a90\uff05\u7684\u4e00\u79cd\u6c34\u679c100\u5343\u514b\u3002\u4e00\u661f\u671f\u540e\u518d\u6d4b\uff0c\u53d1\u73b0\u542b\u6c34\u91cf\u964d\u4f4e\u523080\uff05\u3002\u73b0\u5728\u8fd9\u6279\u6c34\u679c\u7684\u8d28\u91cf\u662f\u591a\u5c11\u5343\u514b\uff1f

100\u00d7\uff081\uff0d90\uff05\uff09\u00f7\uff081\uff0d80\uff05\uff09\uff1d50\u5343\u514b
5\u3001 \u5728100\u5343\u514b\u6d53\u5ea6\u4e3a50\uff05\u7684\u786b\u9178\u6eb6\u6db2\u4e2d\uff0c\u518d\u52a0\u5165\u591a\u5c11\u5343\u514b\u6d53\u5ea6\u4e3a5\uff05\u7684\u786b\u9178\u6eb6\u6db2\u5c31\u53ef\u4ee5\u914d\u5236\u621025\uff05\u7684\u786b\u9178\u6eb6\u6db2\uff1f

100\u00d7\uff0850\uff05\uff0d25\uff05\uff09\u00f7\uff0825\uff05\uff0d5\uff05\uff09\uff1d125\u5343\u514b 6\u3001 \u6d53\u5ea6\u4e3a70\uff05\u7684\u9152\u7cbe\u6eb6\u6db2500\u514b\u4e0e\u6d53\u5ea6\u4e3a50\uff05\u7684\u9152\u7cbe\u6eb6\u6db2300\u514b\u6df7\u5408\u540e\u6240\u5f97\u5230\u7684\u9152\u7cbe\u6eb6\u6db2\u7684\u6d53\u5ea6\u662f\u591a\u5c11\uff1f

\uff08500\u00d770\uff05+300\u00d750\uff05\uff09\u00f7\uff08500+300\uff09\u00d7100\uff05\uff1d62.5\uff05
7\u3001 \u4e24\u79cd\u94a2\u5206\u522b\u542b\u954d5\uff05\u548c40\uff05\uff0c\u8981\u5f97\u5230140\u5428\u542b\u954d30\uff05\u7684\u94a2\uff0c\u9700\u8981\u542b\u954d5\uff05\u7684\u94a2\u548c\u542b\u954d40\uff05\u7684\u94a2\u5404\u591a\u5c11\u5428\uff1f

\u89e3\uff1a\u8bbe\u9700\u542b\u954d5\uff05\u7684\u94a2x\u5428\uff0c\u5219\u542b\u954d40\uff05\u7684\u94a2140\uff0dx\u5428\uff0c 5\uff05x+\uff08140\uff0dx\uff09\u00d740\uff05\uff1d140\u00d730\uff05 X \uff1d40 140\uff0d40\uff1d100\u5428
8\u3001 \u7532\u3001\u4e59\u4e24\u79cd\u9152\u5404\u542b\u9152\u7cbe75\uff05\u548c55\uff05\uff0c\u8981\u914d\u5236\u542b\u9152\u7cbe65\uff05\u7684\u91523000\u514b\uff0c\u5e94\u5f53\u4ece\u8fd9\u4e24\u79cd\u9152\u4e2d\u5404\u53d6\u591a\u5c11\u514b\uff1f
\uff083000\u00d775\uff05\uff0d3000\u00d765\uff05\uff09\u00f7\u30101\u00d7\uff0875\uff05\uff0d55\uff05\uff09\u3011\uff1d1500\u514b 3000\uff0d1500\uff1d1500\u514b
9\u3001 \u4ece\u88c5\u6ee1100\u514b80\uff05\u7684\u76d0\u6c34\u4e2d\u5012\u51fa40\u514b\u76d0\u6c34\u540e\uff0c\u518d\u7528\u6e05\u6c34\u5c06\u676f\u52a0\u6ee1\uff0c\u6405\u62cc\u540e\u518d\u5012\u51fa40\u514b\u76d0\u6c34\uff0c\u7136\u540e\u518d\u7528\u6e05\u6c34\u5c06\u676f\u52a0\u6ee1\u3002\u5982\u6b64\u53cd\u590d\u4e09\u6b21\u540e\uff0c\u676f\u4e2d\u76d0\u6c34\u7684\u6d53\u5ea6\u662f\u591a\u5c11\uff1f

\u89e3\u6cd5\u4e00\uff1a100\u00d780\uff05\uff1d80\u514b 40\u00d780\uff05\uff1d32\u514b \uff0880\uff0d32\uff09\u00f7100\uff1d48\uff05 40\u00d748\uff05\uff1d19.2\u514b \uff0880\uff0d32\uff0d19.2\uff09\u00f7100\uff1d28.8\uff05 40\u00d728.8\uff1d11.52\u514b
\uff0880\uff0d32\uff0d19.2\uff0d11.52\uff09\u00f7100\uff1d17.28\uff05 \u89e3\u6cd5\u4e8c\uff1a80\u00d7\uff081\uff0d40100 \uff09\u00d7\uff081\uff0d40100 \uff09\u00d7\uff081\uff0d40100 \uff09\u00f7100\uff1d17.28\uff05
10\u3001 \u7532\u5bb9\u5668\u4e2d\u67098\uff05\u7684\u76d0\u6c34300\u514b\uff0c\u4e59\u5bb9\u5668\u4e2d\u670912.5\uff05\u7684\u76d0\u6c34120\u514b\u3002\u5f80\u7532\u3001\u4e59\u4e24\u4e2a\u5bb9\u5668\u5206\u522b\u5012\u5165\u7b49\u91cf\u7684\u6c34\uff0c\u4f7f\u4e24\u4e2a\u5bb9\u5668\u4e2d\u76d0\u6c34\u7684\u6d53\u5ea6\u4e00\u6837\u3002\u6bcf\u4e2a\u5bb9\u5668\u5e94\u5012\u5165\u591a\u5c11\u514b\u6c34\uff1f 300\u00d78\uff05\uff1d24\u514b 120\u00d712.5\uff05\uff1d15\u514b
\u89e3\uff1a\u8bbe\u6bcf\u4e2a\u5bb9\u5668\u5e94\u5012\u5165x\u514b\u6c34\u3002 24300+x \uff1d15120+x
X \uff1d180
1.A\u3001B\u3001C\u4e09\u79cd\u76d0\u6c34\u6d53\u5ea6\u5206\u522b\u4e3a20%\uff0c18%\uff0c16%\uff0c\u7528\u8fd9\u4e09\u79cd\u76d0\u6c34\uff0c\u914d\u5236\u6d53\u5ea6\u4e3a18.8%\u7684\u76d0\u6c34100\u514b\uff0c\u5df2\u77e5B\u6bd4C\u591a\u752830\u514b\uff0c\u6c42\u4e09\u79cd\u76d0\u6c34\u5404\u7528\u591a\u5c11\u514b\u3002
\u8bbeC\u7528\u4e86X\u514b\uff0c\u56e0B\u6bd4C\u591a\u752830\u514b\uff0c\u90a3\u4e48B\u5c31\u5e94\u8be5\u662fB=30+X\uff1b\u53c8\u56e0\u4e3a3\u79cd\u76d0\u6c34\u6df7\u5408\u540e\u91cd\u91cf\u4e3a100\uff0c\u90a3\u4e48A=100-(B+C)=70-2X
\u53c8\u56e0\u603b\u7684\u6d53\u5ea6\u4e3a18.8%\uff0c\u90a3\u4e48\u5217\u65b9\u7a0b\u4e3a 20%\u00d7\uff0870-2X)+18%\u00d7(30+X)+16%\u00d7X=100\u00d718.8% X=10
\u5373A=50 B=40 C=10
2.\u7532\u9152\u7cbe\u6d53\u5ea6\u4e3a72%\u3002\u4e59\u9152\u7cbe\u6d53\u5ea6\u4e3a58%\uff0c\u6df7\u5408\u540e\u9152\u7cbe\u6d53\u5ea6\u4e3a62%\uff0c\u5982\u679c\u6bcf\u79cd\u9152\u7cbe\u6bd4\u539f\u6765\u591a\u53d615\u5347\uff0c\u6df7\u5408\u540e\u9152\u7cbe\u6d53\u5ea6\u4e3a63.25%\uff0c\u95ee\u7b2c\u4e00\u6b21\u6df7\u5408\u65f6\uff0c\u7532\u3001\u4e59\u4e24\u79cd\u9152\u7cbe\u5404\u53d6\u4e86\u591a\u5c11\u5347\uff1f
\u8bbe\u7b2c\u4e00\u6b21\u6df7\u5408\u65f6\uff0c\u7532\u3001\u4e59\u4e24\u79cd\u9152\u7cbe\u5404\u53d6\u4e86X\u3001Y\u5347\uff0c\u90a3\u4e48\u7b2c\u4e8c\u6b21\u53d6\u7684\u5c31\u662fX+15 Y+15 \u5217\u65b9\u7a0b\u5f97\uff1a
72%X+58%Y=62%\u00d7(X+Y) 72%\u00d7(X+15)+58%\u00d7(Y+15)=63.25%\u00d7(X+15+Y+15) X=12 Y=30
3\u3001\u67d0\u79cd\u6d53\u5ea6\u7684\u76d0\u6c34\u4e2d\uff0c\u52a0\u5165\u82e5\u5e72\u6c34\u540e\uff0c\u5f97\u5230\u7684\u76d0\u6c34\u6d53\u5ea6\u4e3a20%\uff1b\u5982\u679c\u5728\u65b0\u76d0\u6c34\u4e2d\u518d\u52a0\u5165\u4e0e\u524d\u9762\u76f8\u7b49\u91cd\u91cf\u7684\u76d0\u540e\uff0c\u76d0\u6c34\u7684\u6d53\u5ea6\u4e3a1/3\uff0c\u6c42\u539f\u6765\u76d0\u6c34\u7684\u6d53\u5ea6\u4e0a\u591a\u5c11\uff1f
\u5341\u5b57\u4ea4\u53c9\u6cd5
\u52a0\u5165\u7684\u76d0\u7684\u91cd\u91cf\uff0c\u4e0e20%\u76d0\u6c34\u7684\u91cd\u91cf\u6bd4\u4e3a\uff1a \uff081/3-20%\uff09\uff1a\uff081-1/3\uff09=1:5
\u539f\u6765\u76d0\u6c34\u4e0e20%\u76d0\u6c34\u7684\u91cd\u91cf\u6bd4\u4e3a\uff1a \uff085-1\uff09\uff1a5=4:5
\u5219\uff0c\u539f\u6765\u76d0\u6c34\u6d53\u5ea6\uff0c\u4e0e20%\u7684\u6bd4\u4e3a5:4






\u539f\u6765\u76d0\u6c34\u6d53\u5ea6\uff1a 20%\u00d75/4=1/4
4\u3001\u5546\u5e97\u91cc\u4e70\u6c28\u6c34,\u6c28\u6c34\u4e2d\u542b\u6c2e16%,\u55b7\u6d12\u65f6\u9700\u7a00\u91ca\u4e3a0.15%\u7684\u6c28\u6c34,\u73b0\u8981\u4f7f\u7528320\u5343\u514b\u7a00\u91ca\u540e\u7684\u6c28\u6c34,\u9700\u51c6\u5907\u542b\u6c2e\u4e3a16%\u7684\u6c28\u6c34\u591a\u5c11\u5343\u514b?\u9700\u52a0\u6c34\u591a\u5c11\u5343\u514b?
\u8bbe\u9700\u51c6\u5907\u542b\u6c2e\u4e3a16%\u7684\u6c28\u6c34\u4e3aX\u5343\u514b 16%X=320*0.15%
X=3
\u9700\u52a0\u6c34320-3=317\u5343\u514b
5\u3001\u6709\u4e24\u4e2a\u5bb9\u79ef\u76f8\u540c\u7684\u5bb9\u5668\uff0c\u7532\u5bb9\u5668\u4e2d\u76d0\u4e0e\u6c34\u7684\u6bd4\u662f2\uff1a9\uff0c\u4e59\u5bb9\u5668\u4e2d\u76d0\u4e0e\u6c34\u7684\u6bd4\u662f3\uff1a10\uff0c\u73b0\u5728\u628a\u4e24\u4e2d\u6eb6\u6db2\u6df7\u5408\u5728\u4e00\u8d77\uff0c\u95ee\u73b0\u5728\u76d0\u4e0e\u76d0\u6c34\u7684\u6bd4\u662f\uff08 \uff09
\u82e5\u4e24\u5bb9\u5668\u5bb9\u79ef\u90fd\u4e3aV
\u5219V\u7532(\u76d0)=2/11V V\u7532(\u6c34)=9/11V V\u4e59(\u76d0)=3/13V V\u4e59(\u6c34)=10/13V \u6240\u4ee5\u6df7\u5408\u540e\u76d0\uff1a\u6c34=(2/11V+3/13V):(9/11V+10/13V)=59\uff1a227 \u6240\u4ee5\u76d0\uff1a\u76d0\u6c34=59\uff1a286 \u53c2\u8003\u7b54\u6848\uff1a 1.\u753225\uff0c\u4e5975 2.80.1% 3.0.5 4.1.5\uff05 5.8\uff05

\u6eb6\u8d28\u7684\u91cd\u91cf\uff0b\u6eb6\u5242\u7684\u91cd\u91cf\uff1d\u6eb6\u6db2\u7684\u91cd\u91cf
\u6eb6\u8d28\u7684\u91cd\u91cf\u00f7\u6eb6\u6db2\u7684\u91cd\u91cf\u00d7100%\uff1d\u6d53\u5ea6
\u6eb6\u6db2\u7684\u91cd\u91cf\u00d7\u6d53\u5ea6\uff1d\u6eb6\u8d28\u7684\u91cd\u91cf
\u6eb6\u8d28\u7684\u91cd\u91cf\u00f7\u6d53\u5ea6\uff1d\u6eb6\u6db2\u7684\u91cd\u91cf
\u8bf4\u4e86\u8fd9\u4e48\u591a\uff0c\u5176\u5b9e\u6700\u5e38\u7528\u7684\u662f\u7528\u65b9\u7a0b\u89e3\u6d53\u5ea6\u95ee\u9898
\u6bd4\u5982\u4e24\u79cd\u4e0d\u540c\u6d53\u5ea6\u7684\u6eb6\u6db2\u6df7\u5408\uff0c\u6700\u5e38\u7528\u7684\u516c\u5f0f\u5f62\u5f0f\u662f
\u7532\u6eb6\u6db2\u8d28\u91cf\u00d7\u6d53\u5ea6+\u4e59\u6eb6\u6db2\u8d28\u91cf\u00d7\u6d53\u5ea6=\u603b\u6eb6\u6db2\u8d28\u91cf\u00d7\u6d53\u5ea6

数量关系:浓度=溶质/溶液,溶质=溶液*浓度,溶液=溶质/浓度
浓度问题一般用方程法比较容易理解,主要是找准不变的量,如加多少水是溶质的量不变,列方程是:原溶液总量*浓度=(原溶液量+水X)*浓度;如求加多少溶质,则是水的量不变。还有先加水,后加溶质的;还有两种不同浓度混合的。主要是找出其中的不变的量。

题目呢?
其实浓度问题比较好做,就是三个公式,浓度=溶质/溶液,溶质=溶液*浓度,溶液=溶质/浓度
关键是要看题目中的什么是前后不变的,大多情况下是溶质

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题目呢?

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