system > system > ConTeXt ver: 2023.08.10 02:59 LMTX fmt: 2023.8.14 int: english/english system > system > 'cont-new.mkxl' loaded open source > level 1, order 1, name '/home/xan/bin/context-current/tex/texmf-context/tex/context/base/mkxl/cont-new.mkxl' system > beware: some patches loaded from cont-new.mkiv close source > level 1, order 1, name '/home/xan/bin/context-current/tex/texmf-context/tex/context/base/mkxl/cont-new.mkxl' system > files > jobname './dev', input './dev.tex', result './dev' fonts > latin modern fonts are not preloaded languages > language 'en' is active open source > level 1, order 2, name './dev.tex' modules > 'pgfrcs' is not found modules > 'pgfmat' is not found modules > 'tikz' is loaded open source > level 2, order 3, name '/home/xan/bin/context-current/tex/texmf-context/tex/context/modules/mkxl/m-tikz.mkxl' open source > level 3, order 4, name 'pgfutil-common.tex' close source > level 3, order 4, name 'pgfutil-common.tex' open source > level 3, order 5, name 'pgfutil-context.def' close source > level 3, order 5, name 'pgfutil-context.def' open source > level 3, order 6, name 'pgfrcs.code.tex' open source > level 4, order 7, name 'pgf.revision.tex' close source > level 4, order 7, name 'pgf.revision.tex' close source > level 3, order 7, name 'pgfrcs.code.tex' open source > level 3, order 8, name 'pgfsys.code.tex' open source > level 4, order 9, name 'pgfkeys.code.tex' open source > level 5, order 10, name 'pgfkeyslibraryfiltered.code.tex' close source > level 5, order 10, name 'pgfkeyslibraryfiltered.code.tex' close source > level 4, order 10, name 'pgfkeys.code.tex' cld > stack > cld > stack > use : slot = context.functions.register(f) cld > stack > and : context.functions.unregister(slot) cld > stack > open source > level 4, order 11, name 'pgf.cfg' close source > level 4, order 11, name 'pgf.cfg' Driver file for pgf: pgfsys-luatex.def open source > level 4, order 12, name 'pgfsys-luatex.def' open source > level 5, order 13, name 'pgfsys-common-pdf.def' close source > level 5, order 13, name 'pgfsys-common-pdf.def' close source > level 4, order 13, name 'pgfsys-luatex.def' open source > level 4, order 14, name 'dev.pgf' close source > level 4, order 14, name 'dev.pgf' close source > level 3, order 14, name 'pgfsys.code.tex' open source > level 3, order 15, name 'pgfkeys.code.tex' close source > level 3, order 15, name 'pgfkeys.code.tex' open source > level 3, order 16, name 'pgfsyssoftpath.code.tex' close source > level 3, order 16, name 'pgfsyssoftpath.code.tex' open source > level 3, order 17, name 'pgfsysprotocol.code.tex' close source > level 3, order 17, name 'pgfsysprotocol.code.tex' open source > level 3, order 18, name 'pgfcore.code.tex' open source > level 4, order 19, name 'pgfmath.code.tex' open source > level 5, order 20, name 'pgfmathutil.code.tex' close source > level 5, order 20, name 'pgfmathutil.code.tex' open source > level 5, order 21, name 'pgfmathparser.code.tex' close source > level 5, order 21, name 'pgfmathparser.code.tex' open source > level 5, order 22, name 'pgfmathfunctions.code.tex' close source > level 5, order 22, name 'pgfmathfunctions.code.tex' open source > level 5, order 23, name 'pgfmathfunctions.basic.code.tex' close source > level 5, order 23, name 'pgfmathfunctions.basic.code.tex' open source > level 5, order 24, name 'pgfmathfunctions.trigonometric.code.tex' close source > level 5, order 24, name 'pgfmathfunctions.trigonometric.code.tex' open source > level 5, order 25, name 'pgfmathfunctions.random.code.tex' close source > level 5, order 25, name 'pgfmathfunctions.random.code.tex' open source > level 5, order 26, name 'pgfmathfunctions.comparison.code.tex' close source > level 5, order 26, name 'pgfmathfunctions.comparison.code.tex' open source > level 5, order 27, name 'pgfmathfunctions.base.code.tex' close source > level 5, order 27, name 'pgfmathfunctions.base.code.tex' open source > level 5, order 28, name 'pgfmathfunctions.round.code.tex' close source > level 5, order 28, name 'pgfmathfunctions.round.code.tex' open source > level 5, order 29, name 'pgfmathfunctions.misc.code.tex' close source > level 5, order 29, name 'pgfmathfunctions.misc.code.tex' open source > level 5, order 30, name 'pgfmathfunctions.integerarithmetics.code.tex' close source > level 5, order 30, name 'pgfmathfunctions.integerarithmetics.code.tex' open source > level 5, order 31, name 'pgfmathcalc.code.tex' close source > level 5, order 31, name 'pgfmathcalc.code.tex' open source > level 5, order 32, name 'pgfmathfloat.code.tex' close source > level 5, order 32, name 'pgfmathfloat.code.tex' close source > level 4, order 32, name 'pgfmath.code.tex' open source > level 4, order 33, name 'pgfint.code.tex' close source > level 4, order 33, name 'pgfint.code.tex' open source > level 4, order 34, name 'pgfcorepoints.code.tex' close source > level 4, order 34, name 'pgfcorepoints.code.tex' open source > level 4, order 35, name 'pgfcorepathconstruct.code.tex' close source > level 4, order 35, name 'pgfcorepathconstruct.code.tex' open source > level 4, order 36, name 'pgfcorepathusage.code.tex' close source > level 4, order 36, name 'pgfcorepathusage.code.tex' open source > level 4, order 37, name 'pgfcorescopes.code.tex' close source > level 4, order 37, name 'pgfcorescopes.code.tex' open source > level 4, order 38, name 'pgfcoregraphicstate.code.tex' close source > level 4, order 38, name 'pgfcoregraphicstate.code.tex' open source > level 4, order 39, name 'pgfcoretransformations.code.tex' close source > level 4, order 39, name 'pgfcoretransformations.code.tex' open source > level 4, order 40, name 'pgfcorequick.code.tex' close source > level 4, order 40, name 'pgfcorequick.code.tex' open source > level 4, order 41, name 'pgfcoreobjects.code.tex' close source > level 4, order 41, name 'pgfcoreobjects.code.tex' open source > level 4, order 42, name 'pgfcorepathprocessing.code.tex' close source > level 4, order 42, name 'pgfcorepathprocessing.code.tex' open source > level 4, order 43, name 'pgfcorearrows.code.tex' close source > level 4, order 43, name 'pgfcorearrows.code.tex' open source > level 4, order 44, name 'pgfcoreshade.code.tex' close source > level 4, order 44, name 'pgfcoreshade.code.tex' open source > level 4, order 45, name 'pgfcoreimage.code.tex' close source > level 4, order 45, name 'pgfcoreimage.code.tex' open source > level 4, order 46, name 'pgfcoreexternal.code.tex' close source > level 4, order 46, name 'pgfcoreexternal.code.tex' open source > level 4, order 47, name 'pgfcorelayers.code.tex' close source > level 4, order 47, name 'pgfcorelayers.code.tex' open source > level 4, order 48, name 'pgfcoretransparency.code.tex' close source > level 4, order 48, name 'pgfcoretransparency.code.tex' open source > level 4, order 49, name 'pgfcorepatterns.code.tex' close source > level 4, order 49, name 'pgfcorepatterns.code.tex' open source > level 4, order 50, name 'pgfcorerdf.code.tex' close source > level 4, order 50, name 'pgfcorerdf.code.tex' close source > level 3, order 50, name 'pgfcore.code.tex' open source > level 3, order 51, name 'pgffor.code.tex' close source > level 3, order 51, name 'pgffor.code.tex' open source > level 3, order 52, name 'pgfmoduleplot.code.tex' close source > level 3, order 52, name 'pgfmoduleplot.code.tex' open source > level 3, order 53, name 'tikz.code.tex' open source > level 4, order 54, name 'pgflibraryplothandlers.code.tex' close source > level 4, order 54, name 'pgflibraryplothandlers.code.tex' open source > level 4, order 55, name 'pgfmodulematrix.code.tex' open source > level 5, order 56, name 'pgfmoduleshapes.code.tex' close source > level 5, order 56, name 'pgfmoduleshapes.code.tex' close source > level 4, order 56, name 'pgfmodulematrix.code.tex' open source > level 4, order 57, name 'tikzlibrarytopaths.code.tex' close source > level 4, order 57, name 'tikzlibrarytopaths.code.tex' close source > level 3, order 57, name 'tikz.code.tex' open source > level 3, order 58, name 'pgfmoduleplot.code.tex' close source > level 3, order 58, name 'pgfmoduleplot.code.tex' open source > level 3, order 59, name 'pgfmoduledecorations.code.tex' close source > level 3, order 59, name 'pgfmoduledecorations.code.tex' close source > level 2, order 59, name '/home/xan/bin/context-current/tex/texmf-context/tex/context/modules/mkxl/m-tikz.mkxl' open source > level 2, order 60, name 'tikzlibrarydecorations.markings.code.tex' open source > level 3, order 61, name 'tikzlibrarydecorations.code.tex' close source > level 3, order 61, name 'tikzlibrarydecorations.code.tex' open source > level 3, order 62, name 'pgflibrarydecorations.markings.code.tex' close source > level 3, order 62, name 'pgflibrarydecorations.markings.code.tex' close source > level 2, order 62, name 'tikzlibrarydecorations.markings.code.tex' open source > level 2, order 63, name 'tikzlibrarytrees.code.tex' close source > level 2, order 63, name 'tikzlibrarytrees.code.tex' open source > level 2, order 64, name 'tikzlibrarycalc.code.tex' close source > level 2, order 64, name 'tikzlibrarycalc.code.tex' open source > level 2, order 65, name 'tikzlibraryintersections.code.tex' open source > level 3, order 66, name 'pgflibraryintersections.code.tex' open source > level 4, order 67, name 'pgflibraryfpu.code.tex' close source > level 4, order 67, name 'pgflibraryfpu.code.tex' close source > level 3, order 67, name 'pgflibraryintersections.code.tex' close source > level 2, order 67, name 'tikzlibraryintersections.code.tex' open source > level 2, order 68, name 'tikzlibrarythrough.code.tex' close source > level 2, order 68, name 'tikzlibrarythrough.code.tex' open source > level 2, order 69, name 'tikzlibrarybackgrounds.code.tex' close source > level 2, order 69, name 'tikzlibrarybackgrounds.code.tex' open source > level 2, order 70, name 'tikzlibraryarrows.code.tex' open source > level 3, order 71, name 'pgflibraryarrows.code.tex' close source > level 3, order 71, name 'pgflibraryarrows.code.tex' close source > level 2, order 71, name 'tikzlibraryarrows.code.tex' open source > level 2, order 72, name 'tikzlibraryshapes.geometric.code.tex' open source > level 3, order 73, name 'pgflibraryshapes.geometric.code.tex' close source > level 3, order 73, name 'pgflibraryshapes.geometric.code.tex' close source > level 2, order 73, name 'tikzlibraryshapes.geometric.code.tex' open source > level 2, order 74, name 'tikzlibraryfadings.code.tex' open source > level 3, order 75, name 'pgflibraryfadings.code.tex' fonts > beware: no fonts are loaded yet, using 'lm mono' in box close source > level 3, order 75, name 'pgflibraryfadings.code.tex' close source > level 2, order 75, name 'tikzlibraryfadings.code.tex' open source > level 2, order 76, name 'tikzlibrarydecorations.pathreplacing.code.tex' open source > level 3, order 77, name 'pgflibrarydecorations.pathreplacing.code.tex' close source > level 3, order 77, name 'pgflibrarydecorations.pathreplacing.code.tex' close source > level 2, order 77, name 'tikzlibrarydecorations.pathreplacing.code.tex' open source > level 2, order 78, name 'tikzlibraryshadings.code.tex' open source > level 3, order 79, name 'pgflibraryshadings.code.tex' close source > level 3, order 79, name 'pgflibraryshadings.code.tex' close source > level 2, order 79, name 'tikzlibraryshadings.code.tex' open source > level 2, order 80, name 'tikzlibrarypatterns.code.tex' open source > level 3, order 81, name 'pgflibrarypatterns.code.tex' close source > level 3, order 81, name 'pgflibrarypatterns.code.tex' close source > level 2, order 81, name 'tikzlibrarypatterns.code.tex' open source > level 2, order 82, name 'tikzlibraryfit.code.tex' close source > level 2, order 82, name 'tikzlibraryfit.code.tex' open source > level 2, order 83, name 'tikzlibrarypositioning.code.tex' close source > level 2, order 83, name 'tikzlibrarypositioning.code.tex' open source > level 2, order 84, name 'tikzlibraryshapes.symbols.code.tex' open source > level 3, order 85, name 'pgflibraryshapes.symbols.code.tex' close source > level 3, order 85, name 'pgflibraryshapes.symbols.code.tex' close source > level 2, order 85, name 'tikzlibraryshapes.symbols.code.tex' open source > level 2, order 86, name 'tikzlibrarychains.code.tex' close source > level 2, order 86, name 'tikzlibrarychains.code.tex' modules > 'pgfmath' is not found fonts > preloading latin modern fonts (second stage) fonts > 'fallback modern rm 12pt' is loaded structure > sectioning > section @ level 3 : 0.0.1 -> Proporcionalitat directa structure > sectioning > subject @ level 3 : 0.0.1 -> Preguntes floatblocks > '1' placed (here) floatblocks > order disturbed floatblocks > '2' placed (force) floatblocks > order disturbed floatblocks > '3' placed (force) backend > xmp > using file '/home/xan/bin/context-current/tex/texmf-context/tex/context/base/mkiv/lpdf-pdx.xml' pages > flushing realpage 1, userpage 1, subpage 1 floatblocks > order disturbed floatblocks > '4' placed (force) pages > flushing realpage 2, userpage 2, subpage 2 floatblocks > order disturbed floatblocks > '5' placed (force) tex error > tex error on line 540 in file ./dev.tex: The file ended when scanning an argument. 200 persones en total \par \startitemize [a, packed] \item 2 de 5 persones estan a $A$ \item a cada 4 persones de $A$ li corresponen 3 persones de $B$ \item 20\% s��n de $C$ \item 2/8 s��n de $D$ \stopitemize \par \head 420 persones en total \par \startitemize [a, packed] \item $3/4$ de persones estan a $A$ \item hi ha una correspond��ncia: 3 de $A$ $\leftrightarrow $ 2 de $B$ \item 40\% ��s de $C$ \item de 5 persones, 4 s��n de $D$ \stopitemize \par \head 245 persones \par \startitemize [a, packed] \item $1/5$ de persones s��n de $A$ \item $20\%$ de persones s��n de $B$ \item per cada 7 persones de $A$, n'hi ha 4 de $C$ \item per cada 49 persones, n'hi ha 1 de $D$ \stopitemize \par \head 1800 persones \par \startitemize [a, packed] \item Un $30\%$ ��s de $A$ \item 30 de cada 50 s��n de $B$ \item cada 5 persones de $B$ li corresponen 2 persones de $C$ \item $D$ t�� un 150\% que les persones de $C$ \stopitemize \par \stopitemize \par En tots els casos, digueu quantes persones hi hauria en el subgrup m��s nombr��s si en total hi hagu��s 1000 persones. \stopexercici \par \startexercici [exercici:proporcionalitat-directa-8]{relacionar diagrames} Relacioneu en cada cas els diagrames amb la proporci�� indicada \par \startitemize [A] \par \head Proporcions \par \startitemize [a, packed, columns] \item 2 de 5 \item 20\% \item $3/5$ \item 5 a 10 \stopitemize \par \head Diagrames \par \startitemize [a, packed, columns] \item \starttikzpicture \draw (0,0) -- (5,0); \foreach \x in {0, 1, 2,..., 5} { \draw (\x , -0.2) -- (\x , 0.2); \draw (\x ,-0.2) node[anchor=north] {\x }; } \draw [color=blue!50, line width=2pt] (0,0) -- (1,0); \stoptikzpicture \par \item \starttikzpicture \draw (0,0) -- (5,0); \foreach \x in {0, 1, 2,..., 5} { \draw (\x , -0.2) -- (\x , 0.2); \draw (\x ,-0.2) node[anchor=north] {\x }; } \draw [color=red!50, line width=2pt] (0,0) -- (2,0); \stoptikzpicture \par \item \starttikzpicture \draw (0,0) -- (5,0); \foreach \x in {0, 1, 2,..., 5} { \draw (\x , -0.2) -- (\x , 0.2); \draw (\x ,-0.2) node[anchor=north] {\x }; } \draw [color=green!50, line width=2pt] (0,0) -- (3,0); \stoptikzpicture \par \item \starttikzpicture \draw (0,0) -- (5,0); \foreach \x in {0, 1, 2,..., 5} { \draw (\x , -0.2) -- (\x , 0.2); \draw (\x ,-0.2) node[anchor=north] {\x }; } \draw [color=orange!50, line width=2pt] (0,0) -- (1.6,0); \stoptikzpicture \par \stopitemize \par \stopitemize \par Per a cada proporci��, dibuixeu nous diagrames que tengui longitud 100. \stopexercici \par \par \startexercici [exercici:proporcionalitat-directa-9]{representar a diagrames}Usant el diagrama $5 \times 10$ seg��ent (vegeu la figura~\in [figura:diagrama-punts-5x10]) representeu la informaci�� donada en cada cas. \par \placefigure [force] [figura:diagrama-punts-5x10] {Diagrama de punts $5 \times 10$} { \bTABLE [frame=off,align={middle,lohi},width=fit, offset=2mm] \bTR \bTD \starttikzpicture \foreach \x in {0,...,9} \foreach \y in {0,...,4} { \draw [fill=gray!50] (\x ,\y ) circle (0.25); } \par \stoptikzpicture \eTD \eTR \eTABLE } \par \startitemize [a, columns, packed, four] \item 40\% \item 4 de 5 \item $3/4$ \item 4 a 1 \item 22\% \item $1/8$ \item 5 a 3 \item 3 de 8 \stopitemize \par Si aquestes informacions corresponguessin a mostres de peixos ferits a la mar, calculeu quants peixos malalts hi hauria en una mostra de 3000 peixos en total. \stopexercici \par \startexercici [exercici:proporcionalitat-directa-antic-1]{sou} Na Marta fa feina per hores. Si fent 25 hores de feina, na Marta cobra 625 euros, quant cobrar�� fent 40 hores? Quantes hores hauria de fer na Marta per cobrar exactament 2300 euros? \stopexercici \par \par \startexercici [exercici:proporcionalitat-directa-antic-2]{astronautes} Aquest ��s la bit��cola d'un projecte espacial: \startitemize [4] \item S'enlairen 5 astronautes, amb 200 kg de menjar a una estaci�� espacial \item Al cap de 3 dies, hi ha un relleu: se'n van 2 i en v��nen 3 \item La tripulaci�� resultant es queda durant 5 dies m��s \item Tots els astronautes tornen. L'estaci�� espacial queda buida \stopitemize \par Els bastar�� el menjar que s'enduen al principi si sabem que quatre astronautes mengen en promig 20 kg per dia? \stopexercici \par \startexercici [exercici:proporcionalitat-directa-antic-3]{consum de benzina} El meu cotxe consumeix 4,5 litres cada cent quil��metres. \startitemize [a,text] \item Quants litres consumiria si fes 56 km? \item Si tenc nom��s 7 litres al dip��sit, quin recorregut podria fer?\stopitemize \stopexercici \par \startexercici [exercici:proporcionalitat-directa-antic-4]{temps per trajecte} Per anar de Palma a Campos una persona tarda 32 minuts. Quant tardaria aquesta persona per anar a Inca? Quan dugui 10 minuts despr��s de partir, a quina dist��ncia estar��? \par \bigskip Dades necess��ries: \startitemize [a, packed] \item Dist��ncia Palma-Campos: $38,7 \unit {kilo meter}$ \item Dist��ncia Palma-Inca: $33,4 \unit {kilo meter}$ \stopitemize \stopexercici \par \startexercici [exercici:proporcionalitat-directa-antic-5]{xamp��} Na Carme es pot rentar els cabells durant 48 dies amb un pot de xamp�� de 150 ml. Qu�� necessita per rentar-se'ls durant 3 mesos? \stopexercici \par \startexercici [exercici:proporcionalitat-directa-antic-6]{ensalada de fruites} Per fer una ensalada de fruites, necessitam tallar a bocinets 4 taronges per a cada 10 pl��tans. Quantes taronges hem de tallar a bocinets si disposem de 25 pl��tans? \stopexercici \par \startexercici [exercici:proporcionalitat-directa-antic-7]{pintura} Pintar $50 \unit {square meter}$ de paret costa 625 euros. Quant costaria pintar $420 \unit {square meter}$? Quants metres podrem pintar si nom��s tenim 500 ���? \stopexercici \par \startexercici [exercici:proporcionalitat-directa-antic-8]{c��ries} Segons les estad��stiques, 2 de cada 5 persones tenen c��ries. Si s��n 360 les persones enquestades, quantes tenen c��ries? \stopexercici \par \par \startexercici [exercici:proporcionalitat-directa-antic-9]{retoladors} Tres retoladors costen 4,80 euros. Quant costaran 5 retoladors? \stopexercici \par \startexercici [exercici:proporcionalitat-directa-antic-10]{rellotge} Un rellotge s'ha endarrerit 18 minuts en 6 dies. Quants minuts s'haur�� endarrerit d'aqu�� a 9 dies��? Quants dies han de passar per a qu�� s'endarrereixi tres quarts d'hora? \stopexercici \par \startexercici [exercici:proporcionalitat-directa-antic-11]{tren} Si un tren recorre 430 km en sis hores, llavors quants de quil��metres recorrer�� en nou hores? \stopexercici \par \startexercici [exercici:proporcionalitat-directa-antic-12]{sou} Na Laia treballa de dependenta durant les vacances de Nadal. Per 5 dies de feina cobra 250 ���. Si ha treballat 14 dies, quant cobrar��? \stopexercici \par \startexercici [exercici:proporcionalitat-directa-antic-13]{arbre} Un arbre als 12 mesos mesura 1,54 m d'altura. Si creix��s al mateix ritme tot el temps, quant mesuraria als 24 mesos? \stopexercici \par \startexercici [exercici:proporcionalitat-directa-antic-14]{Comparaci�� de camises} En una botiga tenen dues ofertes: 3 camises a 57 ��� o b�� 5 camises a 92 ���. Quina ��s millor? \stopexercici \par \startexercici [exercici:proporcionalitat-directa-antic-15]{m��quines d'impressi��} Tres m��quines imprimeixen 1500 llibres cada una al mes. Si un empresari compr��s 5 m��quines m��s, quants llibres podr�� imprimir al cap del mes? \stopexercici \par \startexercici [exercici:proporcionalitat-directa-antic-16]{taronja} Una bossa de taronges de 3 kg costa 5,82 ���. Calculeu quant costar�� una bossa de 5 kg. \stopexercici \par \startexercici [exercici:proporcionalitat-directa-antic-17]{examen} Na J��lia ha contestat b�� 14 de les 18 preguntes d���un examen. Quina nota tindr��? \stopexercici \par \startexercici [exercici:proporcionalitat-directa-antic-18]{Dieta recomanada} A un pot de iogurt de 125 g. hi ha una inscripci�� que posa \par \startnarrower [2*middle] \quotation {Contingut en calci 104 mg. (26\% del consum diari recomanat)} \stopnarrower \par \startitemize [a] \item Quants mil��ligrams de calci hauria de prendre (per a arribar al 100\% de la quantitat de calci recomanada)? \item Per tant, quants iogurts hauria de prendre, si no m��s s'aliment��s de iogurts? \stopitemize \stopexercici \par \startexercici [exercici:proporcionalitat-directa-antic-19]{caixes de llibres} A cinc caixes caben 24 llibres de 5 cm. d'ampl��ria. Quants llibres cabrien a deu caixes? I a 21? \stopexercici \par \startexercici [exercici:proporcionalitat-directa-antic-20]{preu dels pol��grafs} Quatre bol��grafs costen 1,20 ���. Completeu aquesta taula: \par \placetable [here,none] [taula:preu-boli] {Preu dels bol��grafs} { \bTABLE [setups={table3:header, table3:frame, table3:style}] \bTR \bTD Bol��grafs \eTD \bTD 1 \eTD \bTD 2 \eTD \bTD 3 \eTD \bTD 4 \eTD \bTD 5 \eTD \bTD 10 \eTD \bTD 15 \eTD \bTD 20 \eTD \bTD 30 \eTD \bTD 50 \eTD \eTR \bTR \bTD ��� \eTD \bTD \eTD \bTD \eTD \bTD \eTD \bTD \eTD \bTD \eTD \bTD \eTD \bTD \eTD \bTD \eTD \bTD \eTD \eTR \eTABLE } \stopexercici \par \startexercici [exercici:proporcionalitat-directa-antic-21]{m��quina embotelladora} Una m��quina embotelladora ha omplert 45 ampolles en 5 minuts. Quant tardar�� en omplir 180 ampolles? Empleneu la taula seg��ent: \par \placetable [here,none] [taula:preu-ampolles] {Preu de les ampolles} { \bTABLE [setups={table3:header, table3:frame, table3:style}] \par \bTR \bTD Ampolles \eTD \bTD 1 \eTD \bTD 2 \eTD \bTD 3 \eTD \bTD 10 \eTD \bTD 20 \eTD \bTD 90 \eTD \bTD 180 \eTD \bTD 200 \eTD \bTD 300 \eTD \bTD 500 \eTD \eTR \bTR \bTD Temps \eTD \bTD \eTD \bTD \eTD \bTD \eTD \bTD \eTD \bTD \eTD \bTD \eTD \bTD \eTD \bTD \eTD \bTD \eTD \eTR \eTABLE } \stopexercici \par \startexercici [exercici:proporcionalitat-directa-antic-22]{Rajoles de xocolata} Quina rajola surt m��s b�� de preu? \par \placefigure [here] [fig:xocolata] {Ofertes de xocolata} {\externalfigure [figs/proporcionalitat-numerica-vs-xocolata.jpeg]} \par \stopexercici \par \page [yes] \subject {Solucions} \par \startitemize [1][distance=0.5cm] \sym {\in [exercici:proporcionalitat-directa-7]} \startitemize [a] \item $A$ t�� 80 persones, $B$ t�� 60 persones, 40 persones s��n de $C$, 50 persones s��n de $D$. Per tant, el subgrup m��s nombr��s ��s l'$A$. \item $A$ t�� 315 persones, $B$ t�� 210 persones, $C$ t�� 168 persones i $D$ t�� 336. Per tant, el subgrup m��s nombr��s ��s el $D$. \item $A$ t�� 49 persones, $B$ t�� 49 persones, $C$ t�� 28 persones i $D$ t�� 5 persones. Per tant, els subgrups m��s nombrosos s��n $A$ i $B$. \item $A$ t�� 540, $B$ t�� 1080 persones, $C$ t�� 432 persones i $D$ t�� $648$ persones. Per tant, el subgrup m��s nombr��s ��s el $B$. \stopitemize \stopitemize \par \stoptext \stoptext 530 \startitemize[1][distance=0.5cm] 531 \sym{\in[exercici:proporcionalitat-directa-7]} \startitemize[a] 532 \item $A$ t�� 80 persones, $B$ t�� 60 persones, 40 persones s��n de $C$, 50 persones s��n de $D$. Per tant, el subgrup m��s nombr��s ��s l'$A$. 533 \item $A$ t�� 315 persones, $B$ t�� 210 persones, $C$ t�� 168 persones i $D$ t�� 336. Per tant, el subgrup m��s nombr��s ��s el $D$. 534 \item $A$ t�� 49 persones, $B$ t�� 49 persones, $C$ t�� 28 persones i $D$ t�� 5 persones. Per tant, els subgrups m��s nombrosos s��n $A$ i $B$. 535 \item $A$ t�� 540, $B$ t�� 1080 persones, $C$ t�� 432 persones i $D$ t�� $648$ persones. Per tant, el subgrup m��s nombr��s ��s el $B$. 536 \stopitemize 537 \stopitemize 538 539 \stoptext