espacio='texto' tipo='texto' fondo='no' color='20303a' dibujar-si='ay1=0' expresión='[20,20]' rastro='no' familia='' intervalo='' pasos='' texto='{\rtf1\uc0{\fonttbl\f0\fcharset0 Times New Roman;\f1\fcharset0 Arial;\f2\fcharset0 Courier New;}{\colortbl\red0\green0\blue144;\red0\green0\blue255;}\f1\fs24\b\cf0 Tria el tipus de problema que prefereixis.\cf1\f2\fs24\b0\par}' decimales='2' fijo='sí' ancho='1' border='' font='Arial Negrita,BOLD,12' info='' ">
espacio='solu' tipo='texto' fondo='no' color='000000' dibujar-si='(ay1=1)' expresión='[20,100]' rastro='no' familia='' intervalo='' pasos='' texto='{\rtf1\uc0{\fonttbl\f0\fcharset0 Times New Roman;\f1\fcharset0 Arial;\f2\fcharset0 Arial;\f3\fcharset0 Arial;\f4\fcharset0 Times New Roman;}{\colortbl\red0\green0\blue255;\red0\green0\blue0;\red255\green0\blue0;}\f1\fs24 La segona empresa compra{\*\mjaformula{\expr num2\decimals 0\fixed0}{\expr &squot;/&squot;\decimals 0\fixed0}{\expr den2\decimals 0\fixed0}}del que deixa la primera, per tant el que\par queda sense vendre{\*\mjaformula{\expr (queda=1)?&squot; es&squot;:&squot; s\u243 n&squot;\decimals 0\fixed0}} 1 -{\*\mjaformula{\fraction{\num{\expr num2\decimals 0\fixed0}}{\den{\expr den2\decimals 0\fixed0}}}} = {\*\mjaformula{\fraction{\num{\expr den2-num2\decimals 0\fixed0}}{\den{\expr den2\decimals 0\fixed0}}}}del que deixa la primera, que{\*\mjaformula{\expr (queda=1)?&squot;equivale&squot;:&squot;equivalen&squot;\decimals 0\fixed0}}\par a {\*\mjaformula{\expr queda\decimals 0\fixed0}} ha. Aleshores, {\*\mjaformula{\fraction{\num 1}{\den{\expr den2\decimals 0\fixed0}}}}del que deixa la primera s\u243 n{\*\mjaformula{\fraction{\num{\expr queda\decimals 0\fixed0}}{\den{\expr den2-num2\decimals 0\fixed0}}}}ha i \b\cf0\par la segona compra {\*\mjaformula{\expr num2\decimals 0\fixed0}\u183 {\fraction{\num{\expr queda\decimals 0\fixed0}}{\den{\expr den2-num2\decimals 0\fixed0}}} = {\fraction{\num{\expr num2*queda\decimals 0\fixed0}}{\den{\expr den2-num2\decimals 0\fixed0}}} = {\expr num2*queda/(den2-num2)\decimals 2\fixed0}}ha\b0\cf1 .\par El que ha comprat la segona m\u233 s el que queda sense vendre s\u243 n{\*\mjaformula{\expr num2*queda/(den2-num2)\decimals 2\fixed0}+{\expr queda\decimals 0\fixed0} = {\expr num2*queda/(den2-num2)+queda\decimals 2\fixed0} ha}\par La primera empresa compra{\*\mjaformula{\expr num1\decimals 0\fixed0}{\expr &squot;/&squot;\decimals 0\fixed0}{\expr den1\decimals 0\fixed0}}del solar, per tant deixa{\*\mjaformula 1 - {\fraction{\num{\expr num1\decimals 0\fixed0}}{\den{\expr den1\decimals 0\fixed0}}} = {\fraction{\num{\expr den1-num1\decimals 0\fixed0}}{\den{\expr den1\decimals 0\fixed0}}}}\par del solar sense comprar, que{\*\mjaformula{\expr (den1-num1=1)?&squot;equivale&squot;:&squot;equivalen&squot;\decimals 0\fixed0}}a{\*\mjaformula{\expr num2*queda/(den2-num2)+queda\decimals 2\fixed0} ha.} Aleshores, {\*\mjaformula{\fraction{\num 1}{\den{\expr den1\decimals 0\fixed0}}}}del solar \par s\u243 n{\*\mjaformula{\fraction{\num{\expr num2*queda/(den2-num2)+queda\decimals 2\fixed0}}{\den{\expr den1-num1\decimals 0\fixed0}}}}ha i\b\cf0 la primera compra {\*\mjaformula{\expr num1\decimals 0\fixed0}\u183 {\fraction{\num{\expr num2*queda/(den2-num2)+queda\decimals 2\fixed0}}{\den{\expr den1-num1\decimals 0\fixed0}}} = {\fraction{\num{\expr num1*(num2*queda/(den2-num2)+queda)\decimals 2\fixed0}}{\den{\expr den1-num1\decimals 0\fixed0}}} = {\expr num1*(num2*queda/(den2-num2)+queda)/(den1-num1)\decimals 2\fixed0} ha.}\cf2\par \fs28 La superf\u237 cie del solar \u233 s {\*\mjaformula{\expr num1*(num2*queda/(den2-num2)+queda)/(den1-num1)\decimals 2\fixed0}+{\expr num2*queda/(den2-num2)\decimals 2\fixed0}+{\expr queda\decimals 0\fixed0} = {\expr num1*(num2*queda/(den2-num2)+queda)/(den1-num1)+num2*queda/(den2-num2)+queda\decimals 2\fixed0}}ha.\cf1\f4\fs28\b0\i{\*\mjaformula{\supix}}\f1\fs24\i0\par \par \par \par \par \par }' decimales='0' fijo='no' ancho='1' border='' font='SansSerif,PLAIN,12' info='' ">
<param name="G_08" value="
espacio='texto' tipo='texto' fondo='no' color='000000' dibujar-si='ay1=2' expresión='[20,20]' rastro='no' familia='' intervalo='' pasos='' texto='{\rtf1\uc0{\fonttbl\f0\fcharset0 Times New Roman;\f1\fcharset0 Arial;\f2\fcharset0 Courier New;}\f1\fs28 L&squot;import de la reparaci\u243 d&squot;un cotxe en un taller \u233 s de{\*\mjaformula{\expr taller\decimals 0\fixed0}}\u8364 , \par sense IVA. Quant puja la factura amb IVA? (L&squot;IVA \u233 s del 21%)\f2\fs24\par \par \par \par \par }' decimales='0' fijo='no' ancho='1' border='' font='SansSerif,PLAIN,14' info='' ">
espacio='texto' tipo='texto' fondo='no' color='000000' dibujar-si='ay1=3' expresión='[20,15]' rastro='no' familia='' intervalo='' pasos='' texto='{\rtf1\uc0{\fonttbl\f0\fcharset0 Times New Roman;\f1\fcharset0 Arial;\f2\fcharset0 Arial;\f3\fcharset0 Courier New;}\f1\fs28 Per un vestit hem pagat{\*\mjaformula{\expr vestido\decimals 0\fixed0}}\u8364 i a l&squot;etiqueta ens indiquen\par que se li ha aplicat una rebaixa del{\*\mjaformula{\expr rebaja\decimals 0\fixed0} %.} \par Quin era el preu del vestit abans del descompte?\par \fs22\i (Arrodoneix el resultat a euros)\f3\fs24\i0\par \par \par \par \par }' decimales='0' fijo='no' ancho='1' border='' font='SansSerif,PLAIN,14' info='' ">
espacio='solu' tipo='texto' fondo='no' color='000000' dibujar-si='(ay1=3)' expresión='[20,130]' rastro='no' familia='' intervalo='' pasos='' texto='{\rtf1\uc0{\fonttbl\f0\fcharset0 Times New Roman;\f1\fcharset0 Arial;\f2\fcharset0 Arial;\f3\fcharset0 Arial;}{\colortbl\red255\green0\blue0;\red0\green0\blue0;}\f1\fs24 Si ens han aplicat un descompte del{\*\mjaformula{\expr rebaja\decimals 0\fixed0}%}, hem pagat el{\*\mjaformula{\expr 100-rebaja\decimals 0\fixed0}}% del\par preu original. Per tant, el preu anterior al descompte era: \fs32\b\cf0\par \par \fs28{\*\mjaformula{\fraction{\num 100 \u183 {\expr vestido\decimals 0\fixed0}}{\den{\expr 100-rebaja\decimals 0\fixed0}}} = {\expr 100*vestido/(100-rebaja)\decimals 2\fixed1} \u8776 {\expr redondea(100*vestido/(100-rebaja))\decimals 0\fixed0}}\u8364 \cf1\fs24\b0\par }' decimales='0' fijo='no' ancho='1' border='' font='SansSerif,PLAIN,12' info='' ">
<param name="G_14" value="
espacio='texto' tipo='texto' fondo='no' color='000000' dibujar-si='ay1=4' expresión='[20,20]' rastro='no' familia='' intervalo='' pasos='' texto='{\rtf1\uc0{\fonttbl\f0\fcharset0 Times New Roman;\f1\fcharset0 Arial;\f2\fcharset0 Courier New;}\f1\fs28 Quina quantitat de vi hi ha emmagatzemat en{\*\mjaformula{\expr cajas\decimals 0\fixed0}}caixes i{\*\mjaformula{\expr partes[part]\decimals 0\fixed0},} \par si cada caixa cont\u233 24 ampolles de tres quarts de litre cada una?\f2\fs24\par \par \par \par }' decimales='0' fijo='no' ancho='1' border='' font='SansSerif,PLAIN,14' info='' ">
espacio='solu' tipo='texto' fondo='no' color='000000' dibujar-si='(ay1=4)' expresión='[20,100]' rastro='no' familia='' intervalo='' pasos='' texto='{\rtf1\uc0{\fonttbl\f0\fcharset0 Times New Roman;\f1\fcharset0 Arial;\f2\fcharset0 Arial;\f3\fcharset0 Arial;\f4\fcharset0 Arial;}{\colortbl\red0\green0\blue255;\red255\green0\blue0;\red0\green0\blue0;}\f1\fs24{\*\mjaformula{\expr cajas\decimals 0\fixed0}}caixes i{\*\mjaformula{\expr partes[part]\decimals 0\fixed0}}s\u243 n {\*\mjaformula{\expr cajas\decimals 0\fixed0} + {\fraction{\num 1}{\den{\expr partesd[part]\decimals 0\fixed0}}} = {\fraction{\num{\expr cajas*partesd[part]+1\decimals 0\fixed0}}{\den{\expr partesd[part]\decimals 0\fixed0}}}}caixes.\par \par Si hi ha{\*\mjaformula{\fraction{\num{\expr cajas*partesd[part]+1\decimals 0\fixed0}}{\den{\expr partesd[part]\decimals 0\fixed0}}}}caixes, cada caixa t\u233 24 ampolles i cada ampolla \u233 s de{\*\mjaformula{\fraction{\num 3}{\den 4}}}de litre, \par en total hi ha\par \fs32\cf0\par \b\cf1\par \fs28{\*\mjaformula{\fraction{\num{\expr cajas*partesd[part]+1\decimals 0\fixed0}}{\den{\expr partesd[part]\decimals 0\fixed0}}} \u183 24 \u183 {\fraction{\num 3}{\den 4}} = {\fraction{\num{\expr cajas*partesd[part]+1\decimals 0\fixed0} \u183 24 \u183 3}{\den{\expr partesd[part]\decimals 0\fixed0} \u183 4}} ={\fraction{\num{\expr 72*(cajas*partesd[part]+1)\decimals 0\fixed0}}{\den{\expr 4*partesd[part]\decimals 0\fixed0}}} = {\expr 18*(cajas*partesd[part]+1)/partesd[part]\decimals 2\fixed0} litres }\fs32\par \par \cf2\fs24\b0\par }' decimales='0' fijo='no' ancho='1' border='' font='SansSerif,PLAIN,12' info='' ">
<param name="G_17" value="
espacio='texto' tipo='texto' fondo='no' color='000000' dibujar-si='ay1=5' expresión='[20,20]' rastro='no' familia='' intervalo='' pasos='' texto='{\rtf1\uc0{\fonttbl\f0\fcharset0 Times New Roman;\f1\fcharset0 Arial;}\f1\fs28 Una font omple un dip\u242 sit en{\*\mjaformula{\expr f1/mcd(f1,partesd[part])\decimals 0\fixed0}{\expr (f1%partesd[part]=0)?&squot;&squot;:&squot;/&squot;\decimals 0\fixed0}{\expr (f1%partesd[part]=0)?&squot;&squot;:partesd[part]/mcd(f1,partesd[part])\decimals 0\fixed0}}hores i una altra en{\*\mjaformula{\expr f2/mcd(f2,partesd[part2])\decimals 0\fixed0}{\expr (f2%partesd[part2]=0)?&squot;&squot;:&squot;/&squot;\decimals 0\fixed0}{\expr (f2%partesd[part2]=0)?&squot;&squot;:partesd[part2]/mcd(f2,partesd[part2])\decimals 0\fixed0}}hores.\par Quina fracci\u243 del dip\u242 sit omple cada una en una hora?\par I les dues juntes? Quant tardaran en omplir-lo les dues a la vegada?\par }' decimales='0' fijo='no' ancho='1' border='' font='SansSerif,PLAIN,14' info='' ">
espacio='solu' tipo='texto' fondo='no' color='000000' dibujar-si='ay1=5' expresión='[20,100]' rastro='no' familia='' intervalo='' pasos='' texto='{\rtf1\uc0{\fonttbl\f0\fcharset0 Times New Roman;\f1\fcharset0 Arial;\f2\fcharset0 Arial;\f3\fcharset0 Arial;\f4\fcharset0 Arial;}{\colortbl\red0\green0\blue255;\red0\green0\blue0;\red255\green0\blue0;}\f1\fs24 Si la primera tarda{\*\mjaformula{\expr f1/mcd(f1,partesd[part])\decimals 0\fixed0}{\expr (f1%partesd[part]=0)?&squot;&squot;:&squot;/&squot;\decimals 0\fixed0}{\expr (f1%partesd[part]=0)?&squot;&squot;:partesd[part]/mcd(f1,partesd[part])\decimals 0\fixed0}}hores en omplir el dip\u242 sit, \par en una hora omplir\u224 {\*\mjaformula{\expr (f1%partesd[part]=0)?1:partesd[part]/mcd(f1,partesd[part])\decimals 0\fixed0}{\expr &squot;/&squot;\decimals 0\fixed0}{\expr f1/mcd(f1,partesd[part])\decimals 0\fixed0}}del mateix.\par Si la segona tarda{\*\mjaformula{\expr f2/mcd(f2,partesd[part2])\decimals 0\fixed0}{\expr (f2%partesd[part2]=0)?&squot;&squot;:&squot;/&squot;\decimals 0\fixed0}{\expr (f2%partesd[part2]=0)?&squot;&squot;:partesd[part2]/mcd(f2,partesd[part2])\decimals 0\fixed0}}hores en omplir el dip\u242 sit, \par en una hora omplir\u224 {\*\mjaformula{\expr (f2%partesd[part2]=0)?1:partesd[part2]/mcd(f2,partesd[part2])\decimals 0\fixed0}{\expr &squot;/&squot;\decimals 0\fixed0}{\expr f2/mcd(f2,partesd[part2])\decimals 0\fixed0}}del mateix.\par \par En una hora les dues juntes ompliran\cf0\par {\*\mjaformula{\fraction{\num{\expr (f1%partesd[part]=0)?1:partesd[part]/mcd(f1,partesd[part])\decimals 0\fixed0}}{\den{\expr f1/mcd(f1,partesd[part])\decimals 0\fixed0}}} + {\fraction{\num{\expr (f2%partesd[part2]=0)?1:partesd[part2]/mcd(f2,partesd[part2])\decimals 0\fixed0}}{\den{\expr f2/mcd(f2,partesd[part2])\decimals 0\fixed0}}} = {\fraction{\num{\expr mcm(f1/mcd(f1,partesd[part]),f2/mcd(f2,partesd[part2]))/(f1/mcd(f1,partesd[part]))*((f1%partesd[part]=0)?1:partesd[part]/mcd(f1,partesd[part]))\decimals 0\fixed0} + {\expr mcm(f1/mcd(f1,partesd[part]),f2/mcd(f2,partesd[part2]/mcd(f2,partesd[part2])))/(f2/mcd(f2,partesd[part2]/mcd(f2,partesd[part2])))*((f2%partesd[part2]=0)?1:partesd[part2]/mcd(f2,partesd[part2]))\decimals 0\fixed0}}{\den{\expr mcm(f1/mcd(f1,partesd[part]),f2/mcd(f2,partesd[part2]))\decimals 0\fixed0}}} = {\fraction{\num{\expr mcm(f1/mcd(f1,partesd[part]),f2/mcd(f2,partesd[part2]))/(f1/mcd(f1,partesd[part]))*((f1%partesd[part]=0)?1:partesd[part]/mcd(f1,partesd[part]))+mcm(f1/mcd(f1,partesd[part]),f2/mcd(f2,partesd[part2]/mcd(f2,partesd[part2])))/(f2/mcd(f2,partesd[part2]/mcd(f2,partesd[part2])))*((f2%partesd[part2]=0)?1:partesd[part2]/mcd(f2,partesd[part2]))\decimals 0\fixed0}}{\den{\expr mcm(f1/mcd(f1,partesd[part]),f2/mcd(f2,partesd[part2]))\decimals 0\fixed0}}}}del dip\u242 sit.\cf1\par \par Per tant, les dues juntes ompliran el dip\u242 sit en\par \cf2\b \fs28{\*\mjaformula{\fraction{\num{\expr mcm(f1/mcd(f1,partesd[part]),f2/mcd(f2,partesd[part2]))\decimals 0\fixed0}}{\den{\expr mcm(f1/mcd(f1,partesd[part]),f2/mcd(f2,partesd[part2]))/(f1/mcd(f1,partesd[part]))*((f1%partesd[part]=0)?1:partesd[part]/mcd(f1,partesd[part]))+mcm(f1/mcd(f1,partesd[part]),f2/mcd(f2,partesd[part2]/mcd(f2,partesd[part2])))/(f2/mcd(f2,partesd[part2]/mcd(f2,partesd[part2])))*((f2%partesd[part2]=0)?1:partesd[part2]/mcd(f2,partesd[part2]))\decimals 0\fixed0}}} = {\expr (mcm(f1/mcd(f1,partesd[part]),f2/mcd(f2,partesd[part2])))/(mcm(f1/mcd(f1,partesd[part]),f2/mcd(f2,partesd[part2]))/(f1/mcd(f1,partesd[part]))*((f1%partesd[part]=0)?1:partesd[part]/mcd(f1,partesd[part]))+mcm(f1/mcd(f1,partesd[part]),f2/mcd(f2,partesd[part2]/mcd(f2,partesd[part2])))/(f2/mcd(f2,partesd[part2]/mcd(f2,partesd[part2])))*((f2%partesd[part2]=0)?1:partesd[part2]/mcd(f2,partesd[part2])))\decimals 2\fixed0} ={\expr ent((mcm(f1/mcd(f1,partesd[part]),f2/mcd(f2,partesd[part2])))/(mcm(f1/mcd(f1,partesd[part]),f2/mcd(f2,partesd[part2]))/(f1/mcd(f1,partesd[part]))*((f1%partesd[part]=0)?1:partesd[part]/mcd(f1,partesd[part]))+mcm(f1/mcd(f1,partesd[part]),f2/mcd(f2,partesd[part2]/mcd(f2,partesd[part2])))/(f2/mcd(f2,partesd[part2]/mcd(f2,partesd[part2])))*((f2%partesd[part2]=0)?1:partesd[part2]/mcd(f2,partesd[part2]))))\decimals 2\fixed0} hores {\expr ((mcm(f1/mcd(f1,partesd[part]),f2/mcd(f2,partesd[part2])))/(mcm(f1/mcd(f1,partesd[part]),f2/mcd(f2,partesd[part2]))/(f1/mcd(f1,partesd[part]))*((f1%partesd[part]=0)?1:partesd[part]/mcd(f1,partesd[part]))+mcm(f1/mcd(f1,partesd[part]),f2/mcd(f2,partesd[part2]/mcd(f2,partesd[part2])))/(f2/mcd(f2,partesd[part2]/mcd(f2,partesd[part2])))*((f2%partesd[part2]=0)?1:partesd[part2]/mcd(f2,partesd[part2])))-ent((mcm(f1/mcd(f1,partesd[part]),f2/mcd(f2,partesd[part2])))/(mcm(f1/mcd(f1,partesd[part]),f2/mcd(f2,partesd[part2]))/(f1/mcd(f1,partesd[part]))*((f1%partesd[part]=0)?1:partesd[part]/mcd(f1,partesd[part]))+mcm(f1/mcd(f1,partesd[part]),f2/mcd(f2,partesd[part2]/mcd(f2,partesd[part2])))/(f2/mcd(f2,partesd[part2]/mcd(f2,partesd[part2])))*((f2%partesd[part2]=0)?1:partesd[part2]/mcd(f2,partesd[part2])))))*60\decimals 0\fixed0} min }\fs24 \cf1\fs28\b0\par }' decimales='0' fijo='no' ancho='1' border='' font='SansSerif,PLAIN,12' info='' ">
<param name="G_20" value="
espacio='texto' tipo='texto' fondo='no' color='000000' dibujar-si='ay1=6' expresión='[20,12]' rastro='no' familia='' intervalo='' pasos='' texto='{\rtf1\uc0{\fonttbl\f0\fcharset0 Times New Roman;\f1\fcharset0 Arial;\f2\fcharset0 Arial;}\f1\fs26 En un magatzem venen caf\u232 en paquets d&squot;{\*\mjaformula 1{\expr &squot;/&squot;\decimals 0\fixed0}{\expr partesd[part]\decimals 0\fixed0} kg} i descafe\u239 nat en \par paquets d&squot;{\*\mjaformula 1{\expr &squot;/&squot;\decimals 0\fixed0}{\expr partesd[part2]\decimals 0\fixed0} kg.} El preu per kg de les dues varietats \u233 s el mateix. \par Un bar ha comprat{\*\mjaformula{\expr f1\decimals 0\fixed0} }paquets de normal i{\*\mjaformula{\expr f2\decimals 0\fixed0}}de descafe\u239 nat, en\par total ha pagat{\*\mjaformula{\expr cafe*(f1/partesd[part]+f2/partesd[part2])\decimals 2\fixed1}}\u8364 . Quin \u233 s el preu del kg de caf\u232 ?\fs28\par }' decimales='0' fijo='no' ancho='1' border='' font='SansSerif,PLAIN,13' info='' ">
Per
practicar 
