一道数学题详细解决方法
发布网友
发布时间：2022-04-24 02:54
共5个回答
热心网友
时间：2023-10-23 04:13
先计算周期为15步,每15步丢了5颗拣了3颗相当于净少了两颗,于是
100/2*15=750步时应该是0颗,但是实际上不是这样的.
因为走到第735步时,口袋还剩2颗,100-735/15*2=2颗.
再走九步到第744步时,拣了1颗丢了3颗恰好没有了,
再走再走一步到第10步时才会再拣1颗,但是第10步已经没有机会了,因为游戏已经结束,第九步走完口袋没有糖了.
做这类题目时,要特别注意剩下不到一个周期时,口袋中的糖数量的变化情况.
以下是走的步数与口袋中的糖的对应关系.(用程序完成的)
arr = {{1, 100}};
For[i = 1, i < 2000, i++,
If[Mod[i, 3] == 0 && Mod[i, 5] != 0,
arr = Append[arr, {i, arr[[-1]][[-1]] - 1}]];
If[Mod[i, 3] == 0 && Mod[i, 5] == 0,
arr = Append[arr, {i, arr[[-1]][[-1]]}]];
If[Mod[i, 3] != 0 && Mod[i, 5] == 0,
arr = Append[arr, {i, arr[[-1]][[-1]] + 1}]];
If[arr[[-1]][[-1]] == 0, Break[]];
]
arr
{1,100},
{3,99},
{5,100},
{6,99},
{9,98},
{10,99},
{12,98},
{15,98},
{18,97},
{20,98},
{21,97},
{24,96},
{25,97},
{27,96},
{30,96},
{33,95},
{35,96},
{36,95},
{39,94},
{40,95},
{42,94},
{45,94},
{48,93},
{50,94},
{51,93},
{54,92},
{55,93},
{57,92},
{60,92},
{63,91},
{65,92},
{66,91},
{69,90},
{70,91},
{72,90},
{75,90},
{78,89},
{80,90},
{81,89},
{84,88},
{85,89},
{87,88},
{90,88},
{93,87},
{95,88},
{96,87},
{99,86},
{100,87},
{102,86},
{105,86},
{108,85},
{110,86},
{111,85},
{114,84},
{115,85},
{117,84},
{120,84},
{123,83},
{125,84},
{126,83},
{129,82},
{130,83},
{132,82},
{135,82},
{138,81},
{140,82},
{141,81},
{144,80},
{145,81},
{147,80},
{150,80},
{153,79},
{155,80},
{156,79},
{159,78},
{160,79},
{162,78},
{165,78},
{168,77},
{170,78},
{171,77},
{174,76},
{175,77},
{177,76},
{180,76},
{183,75},
{185,76},
{186,75},
{189,74},
{190,75},
{192,74},
{195,74},
{198,73},
{200,74},
{201,73},
{204,72},
{205,73},
{207,72},
{210,72},
{213,71},
{215,72},
{216,71},
{219,70},
{220,71},
{222,70},
{225,70},
{228,69},
{230,70},
{231,69},
{234,68},
{235,69},
{237,68},
{240,68},
{243,67},
{245,68},
{246,67},
{249,66},
{250,67},
{252,66},
{255,66},
{258,65},
{260,66},
{261,65},
{264,64},
{265,65},
{267,64},
{270,64},
{273,63},
{275,64},
{276,63},
{279,62},
{280,63},
{282,62},
{285,62},
{288,61},
{290,62},
{291,61},
{294,60},
{295,61},
{297,60},
{300,60},
{303,59},
{305,60},
{306,59},
{309,58},
{310,59},
{312,58},
{315,58},
{318,57},
{320,58},
{321,57},
{324,56},
{325,57},
{327,56},
{330,56},
{333,55},
{335,56},
{336,55},
{339,54},
{340,55},
{342,54},
{345,54},
{348,53},
{350,54},
{351,53},
{354,52},
{355,53},
{357,52},
{360,52},
{363,51},
{365,52},
{366,51},
{369,50},
{370,51},
{372,50},
{375,50},
{378,49},
{380,50},
{381,49},
{384,48},
{385,49},
{387,48},
{390,48},
{393,47},
{395,48},
{396,47},
{399,46},
{400,47},
{402,46},
{405,46},
{408,45},
{410,46},
{411,45},
{414,44},
{415,45},
{417,44},
{420,44},
{423,43},
{425,44},
{426,43},
{429,42},
{430,43},
{432,42},
{435,42},
{438,41},
{440,42},
{441,41},
{444,40},
{445,41},
{447,40},
{450,40},
{453,39},
{455,40},
{456,39},
{459,38},
{460,39},
{462,38},
{465,38},
{468,37},
{470,38},
{471,37},
{474,36},
{475,37},
{477,36},
{480,36},
{483,35},
{485,36},
{486,35},
{489,34},
{490,35},
{492,34},
{495,34},
{498,33},
{500,34},
{501,33},
{504,32},
{505,33},
{507,32},
{510,32},
{513,31},
{515,32},
{516,31},
{519,30},
{520,31},
{522,30},
{525,30},
{528,29},
{530,30},
{531,29},
{534,28},
{535,29},
{537,28},
{540,28},
{543,27},
{545,28},
{546,27},
{549,26},
{550,27},
{552,26},
{555,26},
{558,25},
{560,26},
{561,25},
{564,24},
{565,25},
{567,24},
{570,24},
{573,23},
{575,24},
{576,23},
{579,22},
{580,23},
{582,22},
{585,22},
{588,21},
{590,22},
{591,21},
{594,20},
{595,21},
{597,20},
{600,20},
{603,19},
{605,20},
{606,19},
{609,18},
{610,19},
{612,18},
{615,18},
{618,17},
{620,18},
{621,17},
{624,16},
{625,17},
{627,16},
{630,16},
{633,15},
{635,16},
{636,15},
{639,14},
{640,15},
{642,14},
{645,14},
{648,13},
{650,14},
{651,13},
{654,12},
{655,13},
{657,12},
{660,12},
{663,11},
{665,12},
{666,11},
{669,10},
{670,11},
{672,10},
{675,10},
{678,9},
{680,10},
{681,9},
{684,8},
{685,9},
{687,8},
{690,8},
{693,7},
{695,8},
{696,7},
{699,6},
{700,7},
{702,6},
{705,6},
{708,5},
{710,6},
{711,5},
{714,4},
{715,5},
{717,4},
{720,4},
{723,3},
{725,4},
{726,3},
{729,2},
{730,3},
{732,2},
{735,2},
{738,1},
{740,2},
{741,1},
{744,0}.
热心网友
时间：2023-10-23 04:13
由题意得(a-b)/a=1/4
解得 b/a=3/4
b=（3/4）*a
所以：
(a-b)/b=(1/4)a/(3/4a)=1/3
（羊的只数比牛的头数少百分之几：即牛的头数与羊的只数的差，再除以羊的只数）
热心网友
时间：2023-10-23 04:14
则牛的个数为5x
所以羊比牛烧（5x-4x）/5x=20%
热心网友
时间：2023-10-23 04:14
1.25x—x=0.25x
025x除以1.25x=20%
答：羊比牛少20%。
热心网友
时间：2023-10-23 04:15
热心网友
时间：2023-10-23 04:13
先计算周期为15步,每15步丢了5颗拣了3颗相当于净少了两颗,于是
100/2*15=750步时应该是0颗,但是实际上不是这样的.
因为走到第735步时,口袋还剩2颗,100-735/15*2=2颗.
再走九步到第744步时,拣了1颗丢了3颗恰好没有了,
再走再走一步到第10步时才会再拣1颗,但是第10步已经没有机会了,因为游戏已经结束,第九步走完口袋没有糖了.
做这类题目时,要特别注意剩下不到一个周期时,口袋中的糖数量的变化情况.
以下是走的步数与口袋中的糖的对应关系.(用程序完成的)
arr = {{1, 100}};
For[i = 1, i < 2000, i++,
If[Mod[i, 3] == 0 && Mod[i, 5] != 0,
arr = Append[arr, {i, arr[[-1]][[-1]] - 1}]];
If[Mod[i, 3] == 0 && Mod[i, 5] == 0,
arr = Append[arr, {i, arr[[-1]][[-1]]}]];
If[Mod[i, 3] != 0 && Mod[i, 5] == 0,
arr = Append[arr, {i, arr[[-1]][[-1]] + 1}]];
If[arr[[-1]][[-1]] == 0, Break[]];
]
arr
{1,100},
{3,99},
{5,100},
{6,99},
{9,98},
{10,99},
{12,98},
{15,98},
{18,97},
{20,98},
{21,97},
{24,96},
{25,97},
{27,96},
{30,96},
{33,95},
{35,96},
{36,95},
{39,94},
{40,95},
{42,94},
{45,94},
{48,93},
{50,94},
{51,93},
{54,92},
{55,93},
{57,92},
{60,92},
{63,91},
{65,92},
{66,91},
{69,90},
{70,91},
{72,90},
{75,90},
{78,89},
{80,90},
{81,89},
{84,88},
{85,89},
{87,88},
{90,88},
{93,87},
{95,88},
{96,87},
{99,86},
{100,87},
{102,86},
{105,86},
{108,85},
{110,86},
{111,85},
{114,84},
{115,85},
{117,84},
{120,84},
{123,83},
{125,84},
{126,83},
{129,82},
{130,83},
{132,82},
{135,82},
{138,81},
{140,82},
{141,81},
{144,80},
{145,81},
{147,80},
{150,80},
{153,79},
{155,80},
{156,79},
{159,78},
{160,79},
{162,78},
{165,78},
{168,77},
{170,78},
{171,77},
{174,76},
{175,77},
{177,76},
{180,76},
{183,75},
{185,76},
{186,75},
{189,74},
{190,75},
{192,74},
{195,74},
{198,73},
{200,74},
{201,73},
{204,72},
{205,73},
{207,72},
{210,72},
{213,71},
{215,72},
{216,71},
{219,70},
{220,71},
{222,70},
{225,70},
{228,69},
{230,70},
{231,69},
{234,68},
{235,69},
{237,68},
{240,68},
{243,67},
{245,68},
{246,67},
{249,66},
{250,67},
{252,66},
{255,66},
{258,65},
{260,66},
{261,65},
{264,64},
{265,65},
{267,64},
{270,64},
{273,63},
{275,64},
{276,63},
{279,62},
{280,63},
{282,62},
{285,62},
{288,61},
{290,62},
{291,61},
{294,60},
{295,61},
{297,60},
{300,60},
{303,59},
{305,60},
{306,59},
{309,58},
{310,59},
{312,58},
{315,58},
{318,57},
{320,58},
{321,57},
{324,56},
{325,57},
{327,56},
{330,56},
{333,55},
{335,56},
{336,55},
{339,54},
{340,55},
{342,54},
{345,54},
{348,53},
{350,54},
{351,53},
{354,52},
{355,53},
{357,52},
{360,52},
{363,51},
{365,52},
{366,51},
{369,50},
{370,51},
{372,50},
{375,50},
{378,49},
{380,50},
{381,49},
{384,48},
{385,49},
{387,48},
{390,48},
{393,47},
{395,48},
{396,47},
{399,46},
{400,47},
{402,46},
{405,46},
{408,45},
{410,46},
{411,45},
{414,44},
{415,45},
{417,44},
{420,44},
{423,43},
{425,44},
{426,43},
{429,42},
{430,43},
{432,42},
{435,42},
{438,41},
{440,42},
{441,41},
{444,40},
{445,41},
{447,40},
{450,40},
{453,39},
{455,40},
{456,39},
{459,38},
{460,39},
{462,38},
{465,38},
{468,37},
{470,38},
{471,37},
{474,36},
{475,37},
{477,36},
{480,36},
{483,35},
{485,36},
{486,35},
{489,34},
{490,35},
{492,34},
{495,34},
{498,33},
{500,34},
{501,33},
{504,32},
{505,33},
{507,32},
{510,32},
{513,31},
{515,32},
{516,31},
{519,30},
{520,31},
{522,30},
{525,30},
{528,29},
{530,30},
{531,29},
{534,28},
{535,29},
{537,28},
{540,28},
{543,27},
{545,28},
{546,27},
{549,26},
{550,27},
{552,26},
{555,26},
{558,25},
{560,26},
{561,25},
{564,24},
{565,25},
{567,24},
{570,24},
{573,23},
{575,24},
{576,23},
{579,22},
{580,23},
{582,22},
{585,22},
{588,21},
{590,22},
{591,21},
{594,20},
{595,21},
{597,20},
{600,20},
{603,19},
{605,20},
{606,19},
{609,18},
{610,19},
{612,18},
{615,18},
{618,17},
{620,18},
{621,17},
{624,16},
{625,17},
{627,16},
{630,16},
{633,15},
{635,16},
{636,15},
{639,14},
{640,15},
{642,14},
{645,14},
{648,13},
{650,14},
{651,13},
{654,12},
{655,13},
{657,12},
{660,12},
{663,11},
{665,12},
{666,11},
{669,10},
{670,11},
{672,10},
{675,10},
{678,9},
{680,10},
{681,9},
{684,8},
{685,9},
{687,8},
{690,8},
{693,7},
{695,8},
{696,7},
{699,6},
{700,7},
{702,6},
{705,6},
{708,5},
{710,6},
{711,5},
{714,4},
{715,5},
{717,4},
{720,4},
{723,3},
{725,4},
{726,3},
{729,2},
{730,3},
{732,2},
{735,2},
{738,1},
{740,2},
{741,1},
{744,0}.
热心网友
时间：2023-10-23 04:13
由题意得(a-b)/a=1/4
解得 b/a=3/4
b=（3/4）*a
所以：
(a-b)/b=(1/4)a/(3/4a)=1/3
（羊的只数比牛的头数少百分之几：即牛的头数与羊的只数的差，再除以羊的只数）
热心网友
时间：2023-10-23 04:14
则牛的个数为5x
所以羊比牛烧（5x-4x）/5x=20%
热心网友
时间：2023-10-23 04:14
1.25x—x=0.25x
025x除以1.25x=20%
答：羊比牛少20%。
热心网友
时间：2023-10-23 04:15
热心网友
时间：2023-10-23 04:13
先计算周期为15步,每15步丢了5颗拣了3颗相当于净少了两颗,于是
100/2*15=750步时应该是0颗,但是实际上不是这样的.
因为走到第735步时,口袋还剩2颗,100-735/15*2=2颗.
再走九步到第744步时,拣了1颗丢了3颗恰好没有了,
再走再走一步到第10步时才会再拣1颗,但是第10步已经没有机会了,因为游戏已经结束,第九步走完口袋没有糖了.
做这类题目时,要特别注意剩下不到一个周期时,口袋中的糖数量的变化情况.
以下是走的步数与口袋中的糖的对应关系.(用程序完成的)
arr = {{1, 100}};
For[i = 1, i < 2000, i++,
If[Mod[i, 3] == 0 && Mod[i, 5] != 0,
arr = Append[arr, {i, arr[[-1]][[-1]] - 1}]];
If[Mod[i, 3] == 0 && Mod[i, 5] == 0,
arr = Append[arr, {i, arr[[-1]][[-1]]}]];
If[Mod[i, 3] != 0 && Mod[i, 5] == 0,
arr = Append[arr, {i, arr[[-1]][[-1]] + 1}]];
If[arr[[-1]][[-1]] == 0, Break[]];
]
arr
{1,100},
{3,99},
{5,100},
{6,99},
{9,98},
{10,99},
{12,98},
{15,98},
{18,97},
{20,98},
{21,97},
{24,96},
{25,97},
{27,96},
{30,96},
{33,95},
{35,96},
{36,95},
{39,94},
{40,95},
{42,94},
{45,94},
{48,93},
{50,94},
{51,93},
{54,92},
{55,93},
{57,92},
{60,92},
{63,91},
{65,92},
{66,91},
{69,90},
{70,91},
{72,90},
{75,90},
{78,89},
{80,90},
{81,89},
{84,88},
{85,89},
{87,88},
{90,88},
{93,87},
{95,88},
{96,87},
{99,86},
{100,87},
{102,86},
{105,86},
{108,85},
{110,86},
{111,85},
{114,84},
{115,85},
{117,84},
{120,84},
{123,83},
{125,84},
{126,83},
{129,82},
{130,83},
{132,82},
{135,82},
{138,81},
{140,82},
{141,81},
{144,80},
{145,81},
{147,80},
{150,80},
{153,79},
{155,80},
{156,79},
{159,78},
{160,79},
{162,78},
{165,78},
{168,77},
{170,78},
{171,77},
{174,76},
{175,77},
{177,76},
{180,76},
{183,75},
{185,76},
{186,75},
{189,74},
{190,75},
{192,74},
{195,74},
{198,73},
{200,74},
{201,73},
{204,72},
{205,73},
{207,72},
{210,72},
{213,71},
{215,72},
{216,71},
{219,70},
{220,71},
{222,70},
{225,70},
{228,69},
{230,70},
{231,69},
{234,68},
{235,69},
{237,68},
{240,68},
{243,67},
{245,68},
{246,67},
{249,66},
{250,67},
{252,66},
{255,66},
{258,65},
{260,66},
{261,65},
{264,64},
{265,65},
{267,64},
{270,64},
{273,63},
{275,64},
{276,63},
{279,62},
{280,63},
{282,62},
{285,62},
{288,61},
{290,62},
{291,61},
{294,60},
{295,61},
{297,60},
{300,60},
{303,59},
{305,60},
{306,59},
{309,58},
{310,59},
{312,58},
{315,58},
{318,57},
{320,58},
{321,57},
{324,56},
{325,57},
{327,56},
{330,56},
{333,55},
{335,56},
{336,55},
{339,54},
{340,55},
{342,54},
{345,54},
{348,53},
{350,54},
{351,53},
{354,52},
{355,53},
{357,52},
{360,52},
{363,51},
{365,52},
{366,51},
{369,50},
{370,51},
{372,50},
{375,50},
{378,49},
{380,50},
{381,49},
{384,48},
{385,49},
{387,48},
{390,48},
{393,47},
{395,48},
{396,47},
{399,46},
{400,47},
{402,46},
{405,46},
{408,45},
{410,46},
{411,45},
{414,44},
{415,45},
{417,44},
{420,44},
{423,43},
{425,44},
{426,43},
{429,42},
{430,43},
{432,42},
{435,42},
{438,41},
{440,42},
{441,41},
{444,40},
{445,41},
{447,40},
{450,40},
{453,39},
{455,40},
{456,39},
{459,38},
{460,39},
{462,38},
{465,38},
{468,37},
{470,38},
{471,37},
{474,36},
{475,37},
{477,36},
{480,36},
{483,35},
{485,36},
{486,35},
{489,34},
{490,35},
{492,34},
{495,34},
{498,33},
{500,34},
{501,33},
{504,32},
{505,33},
{507,32},
{510,32},
{513,31},
{515,32},
{516,31},
{519,30},
{520,31},
{522,30},
{525,30},
{528,29},
{530,30},
{531,29},
{534,28},
{535,29},
{537,28},
{540,28},
{543,27},
{545,28},
{546,27},
{549,26},
{550,27},
{552,26},
{555,26},
{558,25},
{560,26},
{561,25},
{564,24},
{565,25},
{567,24},
{570,24},
{573,23},
{575,24},
{576,23},
{579,22},
{580,23},
{582,22},
{585,22},
{588,21},
{590,22},
{591,21},
{594,20},
{595,21},
{597,20},
{600,20},
{603,19},
{605,20},
{606,19},
{609,18},
{610,19},
{612,18},
{615,18},
{618,17},
{620,18},
{621,17},
{624,16},
{625,17},
{627,16},
{630,16},
{633,15},
{635,16},
{636,15},
{639,14},
{640,15},
{642,14},
{645,14},
{648,13},
{650,14},
{651,13},
{654,12},
{655,13},
{657,12},
{660,12},
{663,11},
{665,12},
{666,11},
{669,10},
{670,11},
{672,10},
{675,10},
{678,9},
{680,10},
{681,9},
{684,8},
{685,9},
{687,8},
{690,8},
{693,7},
{695,8},
{696,7},
{699,6},
{700,7},
{702,6},
{705,6},
{708,5},
{710,6},
{711,5},
{714,4},
{715,5},
{717,4},
{720,4},
{723,3},
{725,4},
{726,3},
{729,2},
{730,3},
{732,2},
{735,2},
{738,1},
{740,2},
{741,1},
{744,0}.
热心网友
时间：2023-10-23 04:13
由题意得(a-b)/a=1/4
解得 b/a=3/4
b=（3/4）*a
所以：
(a-b)/b=(1/4)a/(3/4a)=1/3
（羊的只数比牛的头数少百分之几：即牛的头数与羊的只数的差，再除以羊的只数）
热心网友
时间：2023-10-23 04:14
则牛的个数为5x
所以羊比牛烧（5x-4x）/5x=20%
热心网友
时间：2023-10-23 04:14
1.25x—x=0.25x
025x除以1.25x=20%
答：羊比牛少20%。
热心网友
时间：2023-10-23 04:15
