7-Problemas de Misturas de Subst\303\242ncias Vamos estudar a mistura de duas subst\303\242ncias para obter uma quantidade de valor intermedi\303\241rio. Um estudo que nos ensina como misturar caf\303\251, nuts, moedas etc. Veremos representa\303\247\303\265es gr\303\241ficas devidamente escalonadas e examinaremos um m\303\251todo para montar e solucionar estes problemas.

restart; with(plots):

Warning, the name changecoords has been redefined

Mistura := proc( a, ar, b, br) local c,ct,cr,g,as,bs,cs, spacer, bo, co, pa, pb, pc1, pc2, tp, te, r, ch; c := a + b; ct := a*ar + b*br; cr := ct/c; g := 1.6; as := sqrt( a/g); bs := sqrt( b/g); cs := sqrt( c/g); spacer := (as+bs+cs)/10; pa := polygonplot( [ [0,0],[as,0],[as,as*g],[0,as*g] ], color = gold, axes = none): bo := as + spacer; pb := polygonplot( [ [bo, 0],[bo+bs, 0],[bo+bs,bs*g],[bo,bs*g] ], color = green, axes = none): co := bo + spacer*1.5 + bs; r := a/(a+b); ch := r*cs*g; pc1 := polygonplot( [ [co,0],[co+cs,0],[co+cs,ch],[co,ch] ], color = gold, axes = none): pc2 := polygonplot( [ [co,ch],[co+cs,ch],[co+cs,cs*g],[co,cs*g] ], color = green, axes = none): tp := textplot( [ as + spacer/2, max(as,bs)*g/2, `+`]); te := textplot( [ bo + bs + spacer/2, max(as,bs)*g/2, `=`]); display( pa, pb, pc1, pc2, tp, te) end proc: MisturaTeste := proc( a, ar, b, br ) # a = quanity of a, ar = a's rate, and so forth for b local rt, M ; rt := (a*ar + b*br)/(a+b); if( not( (whattype(rt) = integer) or (whattype(rt) = float) or (whattype(rt) = fraction) )) then rt := `?` fi; array( [ [``, `Quantidade *`,` Padr\303\243o`,` = Resultado`], [ `A`, a, ar, a*ar], [ `B`, b, br, b*br], [ `A+B `, a+b, rt, a*ar + b*br] ]); end proc: MisturaTabela1 := proc( a, ar, b, br, cr ) # a = quanity of a, ar = a's rate, and so forth for b local rt, M, equation; rt := (a*ar + b*br)/(a+b); if( not( (whattype(rt) = integer) or (whattype(rt) = float) or (whattype(rt) = fraction) )) then rt := `?` fi; M := array( [ [``, `Quantidade *`,` Padr\303\243o`,` = Resultado`], [ `A`, a, ar, a*ar], [ `B`, b, br, b*br], [ `A+B `, a+b, cr, (a+b)*cr] ]); print(M); print(` `): equation := M[2,4] + M[3,4] = M[4,4]; print( equation ); solve( equation, x); print(x = %); end proc: MisturaTabelaEq := proc( ar, br, cr, c) #||a rate|b rate|c rate|c amount|| local a, b, rt, M, equation; rt := cr ; #(a*ar + b*br)/(a+b); a := x; b := c-a; M := array( [ [``, `Quantidade *`, ` Padr\303\243o`,` = Resultado`], [ `A`, a, ar, a*ar ], [ `B`, b, br, (c-a)*br ], [ `A+B `, c, cr, c*cr ] ]); print(M); print(` `): equation := M[2,4] + M[3,4] = M[4,4]; print( equation ); solve( equation, x); print(` `); print(A = %, B = c-%); print(` `); end proc: MisturaTabelaSol := proc( ar, br, cr, c) #||a rate|b rate|c rate|c amount|| local a, rt, M, equation; rt := cr ; #(a*ar + b*br)/(a+b); a := solve( x*ar + (c-x)*br = c*cr, x); array( [ [``, `Quantidade *`, ` Padr\303\243o`,` = Resultado`], [ `A`, a, ar, a*ar ], [ `B`, c-a, br, (c-a)*br ], [ `A+B `, c, cr, c*cr ] ]); end proc:

Existem algumas varia\303\247\303\265es de problemas de misturas, como as de caf\303\251, gr\303\243os e moedas. Primeiro, vamos apresentar uma id\303\251ia geral dos fatos. ___________________________________________________________________________________________ Problema 1.1 : Misturando 5 quilos de gr\303\243os, que valem R$2 por quilo, e 3 quilos de gr\303\243os, que custam R$4 por quilo. Mistura( 5, 2, 3, 4); #(a amount) | (a rate) | (b amount) | (b rate)

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Podemos computar tr\303\252s itens: 1. Quantos quilos temos na mistura ? 2. Quanto custa a mistura inteira ? 3. Quanto vale o quilo da mistura ? `N\303\272mero total de quilos` := 5 + 3; `Total de custo` := 5*2 + 3*4; `Custo por quilo` := evalf( %/%%, 3) ;

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_______________________________________________________________________________________ Problema 1.2 : Voc\303\252 mistura 12 quilos de caf\303\251 A valendo $5.50 por quilo e 19 quilos de caf\303\251 B valendo $6.75 por quilo. Mistura( 12, 5.50, 19, 6.75 ); #(a amount) | (a rate) | (b amount) | (b rate)

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Podemos computar tr\303\252s itens: 1. Quantos quilos temos na mistura? 2. Quanto custa a mistura inteira? 3. Quanto vale o quilo da mistura? `N\303\272mero total de Quilos` := 12 + 19; `Custo total` := 12*5.50 + 19*6.75; `Custo por quilo` := evalf( %/%%, 3) ;

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_______________________________________________________________________________________ Problema 1.2 : Voc\303\252 mistura 12 quilos de caf\303\251 A valendo $5.50 por quilo e 19 quilos de caf\303\251 B valendo $6.75 por quilo. Observe a diferen\303\247a entre uma mistura 50-50 , uma mistura 99-1 , e uma mistura 1-99. Mistura( 50, 1, 50, 1); Mistura( 99, 1, 1, 1 ); Mistura( 1, 1, 99, 1 );

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Ig==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NiI=

_______________________________________________________________________________________ Problema 1.3 : Voc\303\252 combina 17 moedas de cinco centavos e 23 moedas de vinte e cinco centavos. Quantas moedas voc\303\252 tem? E qual \303\251 o valor total? `n\303\272mero de moedas` = 17 + 23; `valor total` = 17*.05 + 23*.25;

NiMvJTNufGp5fGp2fGh2bWVyb35kZX5tb2VkYXNHIiNTNiMvJSx2YWxvcn50b3RhbEckIiRnJyEiIw==

__________________________________________________________________________________________________ Problema 1.4 : Voc\303\252 combina 12 litros de uma solu\303\247\303\243o de 15% de \303\241cido com 34 litros de uma solu\303\247\303\243o de 22% de \303\241cido.

Problema 2.1 : Quantos quilos do gr\303\243o A que vale R$2 o quilo devem ser misturados com 3 quilos do gr\303\243o B que vale R$4 o quilo para obter uma mistura que custa R$3,50 o quilo? Apenas por divers\303\243o, podemos adivinhar algumas respostas para sentir o problema. Sabemos todas as informa\303\247\303\265es a n\303\243o ser a quantidade do gr\303\243o A. Digamos 3, 5 e 12 quilos de A para ver qual pre\303\247o por quilo aparece no resultado. MisturaTeste( 3, 2, 3, 4); # (a quantity) | (a Raz\303\243o) | (b quantity) | (b rate) MisturaTeste( 5, 2, 3, 4); MisturaTeste( 12, 2, 3, 4);

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Veja o resultado de A+B para cada caso ... R$3 por quilo, R$11/4 = R$2.75 por quilo, e R$12/5 = R$2.40 por quilo. Vamos encontrar a solu\303\247\303\243o. Vamos fazer uma tabela e formar uma equa\303\247\303\243o somando as primeiras duas informa\303\247\303\265es na \303\272ltima coluna para que seja igual \303\240 \303\272ltima infoma\303\247\303\243o, depois solucionar e encontrar a resposta. MisturaTabela1( x, 2, 3, 4, 3.5); #||a amount|a rate|b amount|b rate|c rate||

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__________________________________________________________________________________________________ Problema 2.2 : Quantos quilos de chocolate, que vale R$6.50kg devem ser misturados com 12 kg de chocolate que vale R$11/kg para obter uma mistura que vale R$8 o kg? MisturaTabela1( x, 6.50, 12, 11, 8);

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Problema 2.3 : 100 gramas de um produto qu\303\255mico que vale R$30 o grama devem ser misturados com quantos gramas de um produto que vale R$44 o grama para obter uma mistura que valha R$38 o grama. MisturaTabela1( 100, 30, x, 44, 38);

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NiMlIn5HNiMvLCYiJStJIiIiKiYiI1ciIiIlInhHIiIiIiIiLCYiJStRIiIiKiYiI1EiIiIlInhHIiIiIiIiNiMvJSJ4RyMiJCslIiIk

Problemas com Caf\303\251 e Arroz Problema 3.1 : Quantos quilos do caf\303\251 A, que custa R$8 o quilo, e do caf\303\251 B, que custa R$7,25 o quilo, devem ser misturados para obtermos 50 quilos de uma subst\303\242ncia que custe R$7,70 por quilo? Vamos primeiro criar uma tabela. J\303\241 que ambas as quantidades (de A e B) s\303\243o desconhecidas, precisamos chamar uma de x e a outra de 50-x. E ent\303\243o usamos regra de tr\303\252s, somamos e formamos uma equa\303\247\303\243o. Neste caso: (8x) + (7.25 - 362.50) = 385. Depois \303\251 s\303\263 resolver. MisturaTabelaEq( 8, 7.25, 7.70, 50); #||a rate|b rate|c rate|c amount||

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NiMlIn5HNiMvLCYqJiQiI3YhIiMiIiIlInhHIiIiIiIiJCImXWkkISIjIiIiJCImKyZRISIjNiMlIn5HNiQvJSJBRyQiI0kiIiEvJSJCRyQiIz9GJw==NiMlIn5H

Aqui podemos visualisar a solu\303\247\303\243o: MisturaTabelaSol( 8, 7.25, 7.70, 50 ); #||a rate|b rate|c rate|c amount||

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

Problema 3.2 : Quantos quilos de arroz branco que custa R$2,70 por kg, e arroz integral, que custa R$4,57 por kg, devem ser misturados para obtermos 22 kg de uma mistura que custe $3,55 por kg? Novamente, vamos criar uma tabela. J\303\241 que ambas as quantidades de arroz s\303\243o desconhecidas, precisamos chamar uma de x e a outra de 22-x. Se ent\303\243o usamos regra de tr\303\252s, somamos e formamos uma equa\303\247\303\243o. MisturaTabelaEq( 2.70, 4.57, 3.55, 22); #||a rate|b rate|c rate|c amount||

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NiMlIn5H

Solucionando a equa\303\247\303\243o: -1.87*x + 100.54 = 78.10, para encontrar x, que \303\251 a quantidade de A (Arroz Branco). Descobrimos que A \303\251 12 kg. Para encontrar B (Arroz Integral), subtra\303\255mos isso de 22 para encontrarmos 10 kg. Aqui podemos visualisar a solu\303\247\303\243o: MisturaTabelaSol( 2.60, 4.20, 3.15, 18 ); #||a rate|b rate|c rate|c amount||

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYmLUYjNiUtSSdtdGFibGVHRiQ2OC1JJG10ckdGJDYpLUkkbXRkR0YkNigtSSNtaUdGJDYlUSFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvJSlyb3dhbGlnbkdGPC8lLGNvbHVtbmFsaWduR0Y8LyUrZ3JvdXBhbGlnbkdGPC8lKHJvd3NwYW5HUSIxRicvJStjb2x1bW5zcGFuR0ZLLUY3NigtRjo2JVEvUXVhbnRpZGFkZX5+fipGJ0Y9RkBGQ0ZFRkdGSUZMLUY3NigtRjo2JVEuflBhZHImIzY1NTMzO0YnRj1GQEZDRkVGR0ZJRkwtRjc2KC1GOjYlUS5+PX5+UmVzdWx0YWRvRidGPUZARkNGRUZHRklGTEZDRkVGRy1GNDYpLUY3NigtRjo2JVEiQUYnRj1GQEZDRkVGR0ZJRkwtRjc2KC1JI21uR0YkNiRRLDExLjgxMjUwMDAwRicvRkFRJ25vcm1hbEYnRkNGRUZHRklGTC1GNzYoLUZhbzYkUSUyLjYwRidGZG9GQ0ZFRkdGSUZMLUY3NigtRmFvNiRRLDMwLjcxMjUwMDAwRidGZG9GQ0ZFRkdGSUZMRkNGRUZHLUY0NiktRjc2KC1GOjYlUSJCRidGPUZARkNGRUZHRklGTC1GNzYoLUZhbzYkUSs2LjE4NzUwMDAwRidGZG9GQ0ZFRkdGSUZMLUY3NigtRmFvNiRRJTQuMjBGJ0Zkb0ZDRkVGR0ZJRkwtRjc2KC1GYW82JFEsMjUuOTg3NTAwMDBGJ0Zkb0ZDRkVGR0ZJRkxGQ0ZFRkctRjQ2KS1GNzYoLUY6NiVRJkErQn5+RidGPUZARkNGRUZHRklGTC1GNzYoLUZhbzYkUSMxOEYnRmRvRkNGRUZHRklGTC1GNzYoLUZhbzYkUSUzLjE1RidGZG9GQ0ZFRkdGSUZMLUY3NigtRmFvNiRRJjU2LjcwRidGZG9GQ0ZFRkdGSUZMRkNGRUZHLyUmYWxpZ25HUSVheGlzRicvRkRRKWJhc2VsaW5lRicvRkZRJ2NlbnRlckYnL0ZIUSd8ZnJsZWZ0fGhyRicvJS9hbGlnbm1lbnRzY29wZUdGPy8lLGNvbHVtbndpZHRoR1ElYXV0b0YnLyUmd2lkdGhHRmlzLyUrcm93c3BhY2luZ0dRJjEuMGV4RicvJS5jb2x1bW5zcGFjaW5nR1EmMC44ZW1GJy8lKXJvd2xpbmVzR1Elbm9uZUYnLyUsY29sdW1ubGluZXNHRmR0LyUmZnJhbWVHRmR0LyUtZnJhbWVzcGFjaW5nR1EsMC40ZW1+MC41ZXhGJy8lKmVxdWFscm93c0dRJmZhbHNlRicvJS1lcXVhbGNvbHVtbnNHRl51LyUtZGlzcGxheXN0eWxlR0ZedS8lJXNpZGVHUSZyaWdodEYnLyUwbWlubGFiZWxzcGFjaW5nR0ZhdC8lK2ZvcmVncm91bmRHUShbMCwwLDBdRidGZG9GZG8vJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGaHVGZG8=

Problemas com Moedas Quest\303\265es com moedas s\303\243o semelhantes \303\240s com caf\303\251, chocolate e outras medidas de "pre\303\247o por peso". No caso das moedas, n\303\243o atribuimos um um valor por peso, fornecemos o valor por moeda. Ent\303\243o, em vez de termos um "n\303\272mero de quilogramas" e "pre\303\247o por peso", usaremos "n\303\272mero de moedas" e "valor da moeda". E o resto \303\251 igual, essencialmente. Problema 3.3 : Quantas moedas de um centavo e de vinte e cinco centavos s\303\243o necess\303\241rias para termos 64 moedas valendo $4.72? Observe que tanto o n\303\272mero de moedas de um centavo quanto o de vinte e cinco centavos s\303\243o desconhecidos. (Aten\303\247\303\243o - n\303\243o pelo processo matem\303\241tico, mas pelo processo do Maple. O "valor m\303\251dio" de uma moeda \303\251 o valor total de todas as moedas dividido pelo n\303\272mero total de moedas.) MisturaTabelaEq( .01,.25, 4.72/64 , 64); #||a rate|b rate|c rate|c amount||

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Problema 3.4 : Quantas moedas de dez e de cinco centavos s\303\243o necess\303\241rias para termos 80 moedas valendo $4.35? MisturaTabelaEq( .10,.05, 4.35/80 , 80);

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYmLUYjNiUtSSdtdGFibGVHRiQ2OC1JJG10ckdGJDYpLUkkbXRkR0YkNigtSSNtaUdGJDYlUSFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvJSlyb3dhbGlnbkdGPC8lLGNvbHVtbmFsaWduR0Y8LyUrZ3JvdXBhbGlnbkdGPC8lKHJvd3NwYW5HUSIxRicvJStjb2x1bW5zcGFuR0ZLLUY3NigtRjo2JVEvUXVhbnRpZGFkZX5+fipGJ0Y9RkBGQ0ZFRkdGSUZMLUY3NigtRjo2JVEuflBhZHImIzY1NTMzO0YnRj1GQEZDRkVGR0ZJRkwtRjc2KC1GOjYlUS5+PX5+UmVzdWx0YWRvRidGPUZARkNGRUZHRklGTEZDRkVGRy1GNDYpLUY3NigtRjo2JVEiQUYnRj1GQEZDRkVGR0ZJRkwtRjc2KC1GOjYlUSJ4RidGPUZARkNGRUZHRklGTC1GNzYoLUkjbW5HRiQ2JFElMC4xMEYnL0ZBUSdub3JtYWxGJ0ZDRkVGR0ZJRkwtRjc2KC1GIzYmRmVvLUkjbW9HRiQ2LVExJkludmlzaWJsZVRpbWVzO0YnRmlvLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZlcC8lKXN0cmV0Y2h5R0ZlcC8lKnN5bW1ldHJpY0dGZXAvJShsYXJnZW9wR0ZlcC8lLm1vdmFibGVsaW1pdHNHRmVwLyUnYWNjZW50R0ZlcC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRmRxRmBvRmlvRkNGRUZHRklGTEZDRkVGRy1GNDYpLUY3NigtRjo2JVEiQkYnRj1GQEZDRkVGR0ZJRkwtRjc2KC1GIzYmLUZmbzYkUSM4MEYnRmlvLUZgcDYtUSgmbWludXM7RidGaW9GY3BGZnBGaHBGanBGXHFGXnFGYHEvRmNxUSwwLjIyMjIyMjJlbUYnL0ZmcUZpckZgb0Zpb0ZDRkVGR0ZJRkwtRjc2KC1GZm82JFElMC4wNUYnRmlvRkNGRUZHRklGTC1GNzYoLUYjNiYtRmZvNiRRJTQuMDBGJ0Zpb0Zlci1GIzYmRl1zRl9wRmBvRmlvRmlvRkNGRUZHRklGTEZDRkVGRy1GNDYpLUY3NigtRjo2JVEmQStCfn5GJ0Y9RkBGQ0ZFRkdGSUZMLUY3NihGYnJGQ0ZFRkdGSUZMLUY3NigtRmZvNiRRLjAuMDU0Mzc1MDAwMDBGJ0Zpb0ZDRkVGR0ZJRkwtRjc2KC1GZm82JFEsNC4zNTAwMDAwMDBGJ0Zpb0ZDRkVGR0ZJRkxGQ0ZFRkcvJSZhbGlnbkdRJWF4aXNGJy9GRFEpYmFzZWxpbmVGJy9GRlEnY2VudGVyRicvRkhRJ3xmcmxlZnR8aHJGJy8lL2FsaWdubWVudHNjb3BlR0Y/LyUsY29sdW1ud2lkdGhHUSVhdXRvRicvJSZ3aWR0aEdGaXUvJStyb3dzcGFjaW5nR1EmMS4wZXhGJy8lLmNvbHVtbnNwYWNpbmdHUSYwLjhlbUYnLyUpcm93bGluZXNHUSVub25lRicvJSxjb2x1bW5saW5lc0dGZHYvJSZmcmFtZUdGZHYvJS1mcmFtZXNwYWNpbmdHUSwwLjRlbX4wLjVleEYnLyUqZXF1YWxyb3dzR0ZlcC8lLWVxdWFsY29sdW1uc0dGZXAvJS1kaXNwbGF5c3R5bGVHRmVwLyUlc2lkZUdRJnJpZ2h0RicvJTBtaW5sYWJlbHNwYWNpbmdHRmF2LyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJ0Zpb0Zpby8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0Znd0Zpbw==NiMlIn5HNiMvLCYqJiQiIiYhIiMiIiIlInhHIiIiIiIiJCIkKyUhIiMiIiIkIisrKytdViEiKg==NiMlIn5HNiQvJSJBRyQiIigiIiEvJSJCRyQiI3RGJw==NiMlIn5H