import{E as G,c as H,aj as J,T as O,h as d,r as k,ai as V,f as t,b5 as g,a as v,W as l,bI as T,bJ as D,aL as M,m as x,ku as W,s as Q,l as z}from"./index-XCg2QAX4.js";import{b as K}from"./Personne-YG14ggow.js";import{t as i}from"./style-MaFG70fX.js";let U="Solve a proportionality problem with linearity properties";const ee=!0,te="mathLive",se=!0,ie="AMCHybride",re="23/02/2022",oe="c511f",ae="6P11-1";function $e(){G.call(this),this.beta=!1,this.beta?this.nbQuestions=3:this.nbQuestions=1,this.consigne="",H.isHtml?this.spacing=2:this.spacing=1,this.nbCols=1,this.nbColsCorr=1,H.isAmc&&(U="Solve a proportionality problem"),this.nouvelleVersion=function(){const E=[];this.listeQuestions=[],this.listeCorrections=[],this.autoCorrection=[];const F=J(O(0,4),this.nbQuestions),n=K(6),I=[{lieu:"At the bakery",achat_sing:"chocolate bread",achat_plur:"chocolate bread",pu:d([.7,.75,.8,.85])},{lieu:"At the bakery",achat_sing:"croissant",achat_plur:"croissants",pu:d([1.05,1.15,.95,1.25])},{lieu:"At the bakery",achat_sing:"baguette",achat_plur:"chopsticks",pu:d([.9,1.3,1.1,1.2])},{lieu:"At the supermarket",achat_sing:"bottle of fruit juice",achat_plur:"fruit juice bottles",pu:d([1.8,1.9,2.1,2.3])},{lieu:"At the charcuterie",achat_sing:"slice of ham",achat_plur:"Ham slices",pu:d([1.6,1.7,2.2,2.4])}];for(let p=0,y,m,L=0;p<this.nbQuestions&&L<50;){const a=function(C,P){return C>1?P.achat_plur:P.achat_sing};let h=0,S=0,r,s,$,b,c,u,w,A;do{s=k(2,8),r=k(s+1,9,[s,2*s,3*s,4*s]),$=r+s,b=r-s;do w=d([r,s]),A=k(2,5),c=A*w;while(c===b||c===$);u=k(10,19,[$,c])}while(b===1);const e=I[F[p]],o=V([$,b,c]);y=`${e.lieu}, ${n[0]} bought $${r}$ ${a(r,e)} and paid $${i(r*e.pu)}$${t()}€.
      <br>${n[1]} bought $${s}$ ${a(s,e)} and paid $${i(s*e.pu)}$${t()}€.`;const N=`<br>${g(h++)} How much will ${n[2]} pay for $${o[h-1]}$ ${a(o[h-1],e)}? ${v(this,4*p,"largeur25 inline",{texteApres:t(2)+"€"})}`;let f=y+"<br>"+N;y+=N;const _=[{type:"AMCNum",propositions:[{texte:m,statut:"",reponse:{texte:f,valeur:l(o[0]*e.pu,2),param:{digits:T(l(o[0]*e.pu,2)),decimals:D(l(o[0]*e.pu,2)),signe:!1,approx:0}}}]}];f=`${g(h++)} How much will ${n[3]} pay for $${o[h-1]}$ ${a(o[h-1],e)}? ${v(this,4*p+1,"largeur25 inline",{texteApres:t(2)+"€"})}`,y+="<br>"+f,_.push({type:"AMCNum",propositions:[{texte:"",statut:"",reponse:{texte:f,valeur:l(o[1]*e.pu,2),param:{digits:T(l(o[1]*e.pu,2)),decimals:D(l(o[1]*e.pu,2)),signe:!1,approx:0}}}]}),f=`${g(h++)} How much will ${n[4]} pay for $${o[h-1]}$ ${a(o[h-1],e)}? ${v(this,4*p+2,"largeur25 inline",{texteApres:t(2)+"€"})}`,y+="<br>"+f,_.push({type:"AMCNum",propositions:[{texte:"",statut:"",reponse:{texte:f,valeur:l(o[2]*e.pu,2),param:{digits:T(l(o[2]*e.pu,2)),decimals:D(l(o[2]*e.pu,2)),signe:!1,approx:0}}}]}),f=`${g(h++)} What is the maximum number of ${e.achat_plur}s that ${n[5]} can buy with $${i(u*e.pu)}$${t()}€? ${v(this,4*p+3,"largeur25 inline",{texteApres:t(2)+e.achat_plur})}`,y+="<br>"+f,_.push({type:"AMCNum",propositions:[{texte:"",statut:"",reponse:{texte:f,valeur:u,param:{digits:2,decimals:0,signe:!1,approx:0}}}]}),m=`
        It is a situation of proportionality. We can therefore use the linearity properties of proportionality.
        <br>This is what we are going to do for the first three questions.
        <br>`;const j=`
        For $${r}$ ${a(r,e)}, we pay $${i(r*e.pu)}$${t()}€.
        <br> For $${s}$ ${a(s,e)}, we pay $${i(s*e.pu)}$${t()}€.`,R=`
        <br> So for $${r}$ ${a($,e)} $+$ $${s}$ ${a($,e)}, we pay $${i(r*e.pu)}$${t()}€ + $${i(s*e.pu)}$${t()}€.
        <br> ${M(`${n[2]} will therefore pay $${x(i($*e.pu))}$${t()}€ for $${x($)}$ ${a($,e)}.`)}
        <br>`,q=`
        <br> So for $${r}$ ${a($,e)} $-$ $${s}$ ${a(b,e)}, we pay $${i(r*e.pu)}$${t()}€ - $${i(s*e.pu)}$${t()}€.
        <br> ${M(`${n[3]} will therefore pay $${x(i(b*e.pu))}$${t()}€ for $${x(b)}$ ${a(b,e)}.`)}
        <br>`,B=`
        <br> So for $${A}\\times${w}$ ${a(c,e)}, we pay $${A}\\times${i(w*e.pu)}$${t()}€.
        <br> ${M(`${n[4]} will therefore pay $${x(i(c*e.pu))}$${t()}€ for $${x(c)}$ ${a(c,e)}.`)}
        <br>`;for(let C=0;C<3;C++)switch(m+=`<br>${g(S++)}`+j,o[C]){case $:m+=R;break;case b:m+=q;break;case c:m+=B;break}m+=`<br>
        ${g(S++)} We can use one or other of the information in the statement to respond by returning to the unit.
        <br> For example, for $${r}$ ${a(r,e)}, we pay $${i(r*e.pu)}$${t()}€.
        <br> Therefore $1$ ${e.achat_sing} cost $${i(r*e.pu)}$${t()}€ $\\div ${r} = ${i(e.pu)}$${t()}€.
        <br> For $${i(u*e.pu)}$${t()}€, we will therefore have $${i(u*e.pu)}$ ${t()}€ $\\div ${i(e.pu)}$${t()}€ $= ${u}$.
        <br> ${M(`With $${x(i(u*e.pu))}$${t()}€, ${n[5]} can therefore buy $${x(u)}$ ${a(u,e)}.`)}
        `,E.indexOf(W(n[3],$,s,u))===-1&&(E.push(W(n[3],$,s,u)),H.isAmc?this.autoCorrection[p]={enonce:"",enonceAvant:!1,options:{barreseparation:!0,multicolsAll:!0},propositions:_}:(Q(this,4*p,l(o[0]*e.pu,2)),Q(this,4*p+1,l(o[1]*e.pu,2)),Q(this,4*p+2,l(o[2]*e.pu,2)),Q(this,4*p+3,u)),this.listeQuestions.push(y),this.listeCorrections.push(m),p++),L++}z(this)}}export{se as amcReady,ie as amcType,re as dateDeModifImportante,$e as default,ee as interactifReady,te as interactifType,ae as ref,U as titre,oe as uuid};
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