import{E as z,q as w,au as B,ap as Q,C as W,n as T,o as L,K as D,aM as E,ag as F,h as M,c as C,bp as S,g as q,U as k,w as y,W as N,a as H,f as j,bI as G,s as V,l as J}from"./index-ajJ0B2-K.js";import{b as K}from"./Personne-zmVSe1SX.js";import{t as I}from"./style-YtQgMMZt.js";import{a as f,r as x}from"./outilsMathjs-Jea_v8co.js";import"./create-Lu60bgU2.js";const te="Equate a problem and solve it",se=!0,re="mathLive",ae=!0,ne="AMCHybride",ie="15/02/2022",oe="06/04/2023",$e="22412",he="3L13-3";class le extends z{constructor(){super(),this.nbQuestions=2,this.besoinFormulaireTexte=["Choice of problems",`Numbers separated by hyphens
1: basket
2: basket2
3: purchases
4: polygon
5: programs (product vs product,
 ... positive integer solution)
6: programs (product vs product,
 ... negative integer solution)
7: programs (sum vs product,
 ... positive integer solution)
8: programs (sum vs product,
 ... negative integer solution)
9: prices
10: show
11: isosceles
12: Thales
13: Thales2
14: Mixture`],this.sup="14",this.besoinFormulaire2CaseACocher=["Only integers"],this.sup2=!1}figureThales(d,b,v,u){const p=w(1.5,0,"O"),$=w(4,6,"B"),s=w(0,5,"A"),t=B($,p,.4,"D"),a=B(s,p,.4,"C"),r=Q(p,a,s,$,t),e=W(a,t),o=T(`${u}`,.5,1),m=T(`${b}`,0,3),i=T(`${v}`,2,6),c=T(`${d}`,1.5,2.5);return L({xmin:-1,xmax:5,ymin:-1,ymax:7,pixelsParCm:20,scale:.8,zoom:1},r[0],r[1],o,m,i,c,e)}triangleIsocele1(){const d=w(6,1.5),b=w(0,0),v=w(0,3),u=D(d,v,b),p=E("//","black",d,v,d,b);return L({xmin:-1,xmax:7,ymin:-1,ymax:4,pixelsParCm:20,scale:.8,zoom:1},u,p)}triangleIsocele2(){const d=w(3,1.5),b=w(6,0),v=w(0,0),u=D(d,v,b),p=E("//","black",d,v,d,b);return L({xmin:-1,xmax:7,ymin:-1,ymax:2.5,pixelsParCm:20,scale:.8,zoom:1},u,p)}nouvelleVersion(){this.listeQuestions=[],this.listeCorrections=[],this.autoCorrection=[];const d=F({saisie:this.sup,min:1,max:12,melange:14,defaut:1,shuffle:!0,nbQuestions:this.nbQuestions});for(let b=0,v=0,u,p,$,s,t,a,r,e,o,m,i,c,l,n,g,A;b<this.nbQuestions&&v<50;){const h=K(2),O=M(["strawberries","peaches","pears","apples","mangoes","plums","lemons"]),R=["triangle","quadrilateral","Pentagon","hexagon"],P=["film club","fitness club","ski club"];switch(u=["","",""],d[b]){case 1:e=f({x:"randomInt(5,15)",a:"randomInt(5,12)",b:"randomInt(15,30)",d:"b+(a+x)*2+x*3"},{valueOf:!0,type:"number"}),$=e.x,s=e.a,t=e.b,a=0,r=e.d,l=`x*3+(${s}+x)*2+${t} = ${r}`,n=x(l,{reduceSteps:!1,substeps:!0,comment:!0}),o=`A basketball team scored ${r} points during a match. During this match, she scored ${t} points on free throws.<br>`,o+=`The ${s} team scored more two-point baskets than three-point baskets.<br>How many three-point baskets did it score?`,i=`Let $x$ be the number of three-point baskets.<br>The number of two-point baskets is therefore $${s}+x$.<br>`,i+="The team score therefore provides the equation: <br>",c=`<br>The team therefore scored ${$} three-point baskets.`,m="",g=`<br>Verification:<br>$${n.verifLeftSide.printExpression} = ${n.verifLeftSide.printResult}$`;break;case 2:e=f({x:"randomInt(17,27)",a:"randomInt(5,12)",b:"randomInt(15,30)",d:"b+(x-a)*3+x*2"},{valueOf:!0}),$=e.x,s=e.a,t=e.b,r=e.d,a=0,l=`x*2+(x-${s})*3+${t} = ${r}`,n=x(l,{reduceSteps:!1,substeps:!0,comment:!0,suppr1:!1}),o=`A basketball team scored ${r} points during a match. During this match, she scored ${t} points on free throws.<br>`,o+=`The ${s} team scored fewer three-point baskets than two-point baskets.<br>How many two-point baskets did it score?`,i=`Let $x$ be the number of two-point baskets.<br>The number of three-point baskets is therefore $x-${s}$.<br>`,i+="The team score therefore provides the equation: <br>",c=`<br>The team therefore scored ${$} two-point baskets.`,m="",g=`<br>Verification:<br>$${n.verifLeftSide.printExpression} = ${n.verifLeftSide.printResult}$`;break;case 3:e=f({a:`randomInt(2,5)${this.sup2?"":"+randomInt(0,4)/5"}`,x:`randomInt(2,5)${this.sup2?"":"+randomInt(0,1)/2"}`,b:"a*x",test:"b<100 and b>5 and b%10!=0"},{valueOf:!0}),$=e.x,s=e.a,t=e.b,r=t>50?100:t>20?50:t>10?20:10,a=0,l=`${s}*x+${N(r-t,2)} = ${r}`,n=x(l,{substeps:!0,comment:!0}),o=`${h[0]} bought $${y(s)}$ kg of ${O} with a $${r}$ € note. The merchant gave him back $${I(r-t)}$ €.<br>`,o+=`What is the price of a kilogram of ${O}?`,i=`Let $x$ be the price of a kilogram of ${O}.<br>The statement translates into the following equation:<br>`,c=`<br>The price of a kilogram of ${O} is therefore $${y($)}$ €.`,m="",g=`<br>Verification:<br>$${n.verifLeftSide.printExpression} = ${n.verifLeftSide.printResult}$`,u[2]="€";break;case 4:e=f({x:`randomInt(2,4)${this.sup2?"":"+randomInt(0.45)/5"}`,a:`randomInt(2,5)${this.sup2?"":"+randomInt(0.45)/5"}`,b:"randomInt(2,5)",d:"b*x+a"},{valueOf:!0}),$=e.x,s=e.a,t=e.b,r=e.d,a=0,l=`${t}*x+${s} = ${k(r).replace(",",".").replace(/\s+/g,"")}`,n=x(l,{reduceSteps:!0,substeps:!1,comment:!0}),o=`A ${R[t-2]} has one side of length $${y(s)}$ cm and all its other sides have the same length.<br>Its perimeter is $${y(r)}$ cm.<br>`,o+="What is the length"+(C.isAmc?", in cm,":"")+" sides of the same length?",i="Let $x$ be the length of the sides of the same length.<br>",i+=`A ${R[t-2]} has ${t+1} sides, so this one has ${t} sides of the same length.<br>`,i+="The statement translates into the following equation:<br>",c=`<br>The sides of the same length therefore measure $${y($)}$ cm.`,m="",g=`<br>Verification:<br>$${n.verifLeftSide.printExpression} = ${n.verifLeftSide.printResult}$`,u=[" units[Lengths]",new S($,"cm"),""];break;case 5:e=f({a:"randomInt(2,15)",b:"randomInt(1,10)",c:"randomInt(2,15)",d:"randomInt(1,10)",test:"abs((c*d-a*b))%abs(a-c) == 0 and (c*d-a*b)*(a-c)>0"},{valueOf:!0});case 6:d[b]===6&&(e=f({a:"randomInt(2,15)",b:"randomInt(1,10)",c:"randomInt(2,15)",d:"randomInt(1,10)",test:"abs((c*d-a*b))%abs(a-c) == 0 and (c*d-a*b)*(a-c)<0"},{valueOf:!0})),s=e.a,t=e.b,a=e.c,r=e.d,$=Math.round((a*r-s*t)/(s-a)),l=`(x+${t})*${s}=(x+${r})*${a}`,n=x(l,{reduceSteps:!1,substeps:!1,comment:!0}),o=`${h[0]} and ${h[1]} choose the same number.<br> ${h[0]} adds ${t} to it then multiplies the result by ${s} while `,o+=`${h[1]} adds ${r} to it then multiplies the result by ${a}.<br>`,o+=`${h[0]} and ${h[1]} achieve the same result.<br>`,o+=`What common number did ${h[0]} and ${h[1]} choose?`,i="Let $x$ be the number chosen at the start.<br>",i+=`The calculation program carried out by ${h[0]} translates into: $(x+${t})\\times ${s}$.<br>`,i+=`The calculation program carried out by ${h[1]} translates into: $(x+${r})\\times ${a}$.<br>`,i+="The equality of results results in the following equation:<br>",c=`<br>${h[0]} and ${h[1]} we therefore initially chose the ${$} number.`,m="",g=`<br>Verification:<br>On the one hand: $${n.verifLeftSide.printExpression} = ${n.verifLeftSide.printResult}$<br>On the other hand: $${n.verifRightSide.printExpression} = ${n.verifRightSide.printResult}$`;break;case 7:e=f({a:"randomInt(2,15)",b:"randomInt(1,10)",c:"randomInt(2,15)",d:"randomInt(1,10)",test:"abs((d-a*b))%abs(a-c) == 0 and (d-a*b)*(a-c)>0"},{valueOf:!0});case 8:d[b]===8&&(e=f({a:"randomInt(2,15)",b:"randomInt(1,10)",c:"randomInt(2,15)",d:"randomInt(1,10)",test:"abs((d-a*b))%abs(a-c) == 0 and (d-a*b)*(a-c)<0"},{valueOf:!0})),s=e.a,t=e.b,a=e.c,r=e.d,$=Math.round((r-s*t)/(s-a)),l=`(x+${t})*${s} = ${a}*x+${r}`,n=x(l,{reduceSteps:!1,substeps:!1,comment:!0}),o=`${h[0]} and ${h[1]} choose the same number.<br> ${h[0]} adds ${t} to it then multiplies the result by ${s} while `,o+=`${h[1]} multiplies it by ${a} then adds to the result ${r}.<br>`,o+=`${h[0]} and ${h[1]} achieve the same result.<br>`,o+=`What common number did ${h[0]} and ${h[1]} choose?`,i="Let $x$ be the number chosen at the start.<br>",i+=`The calculation program carried out by ${h[0]} translates into: $(x+${t})\\times ${s}$.<br>`,i+=`The calculation program carried out by ${h[1]} translates into: $${a}x + ${r}$.<br>`,i+="The equality of results results in the following equation:<br>",c=`<br>${h[0]} and ${h[1]} we therefore initially chose the ${$} number.`,m="",g=`<br>Verification:<br>On the one hand: $${n.verifLeftSide.printExpression} = ${n.verifLeftSide.printResult}$<br>On the other hand: $${n.verifRightSide.printExpression} = ${n.verifRightSide.printResult}$`;break;case 9:e=f({a:"randomInt(0,2)",b:this.sup2?"randomInt(5,8)":"randomInt(50,80)/10",c:"randomInt(4,10)*5",d:`b-${this.sup2?"randomInt(1,3)":"randomInt(2,6)*0.5"}`,test:"c/(b-d)<30 and c/(b-d)>10 and (c*2)%((b-d)*2)==0"},{valueOf:!0}),s=e.a,t=e.b,a=e.c,r=e.d,$=Math.ceil(a/(t-r)),l=`x*${t}>=${a}+x*${k(r).replace(",",".").replace(/\s+/g,"")}`,n=x(l,{reduceSteps:!1,substeps:!1,comment:!0}),o=`The ${P[s]} of a village offers two prices to its practitioners.<br>`,o+=`Rate A offers to pay $${I(t)}$ € at each session.<br>`,o+=`Rate B offers to pay an annual subscription of $${I(a)}$ € then to pay $${I(r)}$ € per session.<br>`,o+="For what number of sessions does rate B become more advantageous than rate A?",i="Let $x$ be the number of sessions.<br>",i+=`The price to pay with rate A is: $x\\times ${I(t)}$.<br>`,i+=`The price to pay with rate B is: $${I(a)}+x\\times ${I(r)}$.<br>`,i+="For fare B to be more advantageous, $x$ must satisfy the following inequality:<br>",c=`<br>It is from $${$}$ sessions that rate B becomes more advantageous than rate A (for $${$}$ sessions, the two rates are equivalent).`,m="",g=`<br>Verification:<br>On the one hand: $${n.verifLeftSide.printExpression} = ${n.verifLeftSide.printResult}$<br>On the other hand: $${n.verifRightSide.printExpression} = ${n.verifRightSide.printResult}$`;break;case 10:e=f({a:"randomInt(200,300)*10",b:this.sup2?"randomInt(10,20)":"randomInt(100,200)/10",c:this.sup2?"randomInt(5,15)":"randomInt(50,150)/10",x:"randomInt(1000,a-500)",d:"b*x+(a-x)*c",test:"b>c"},{valueOf:!0}),s=e.a,t=e.b,a=e.c,r=e.d,$=e.x,l=`x*${t}+(${s}-x)*${a} = ${k(r).replace(",",".").replace(/\s+/g,"")}`,n=x(l,{reduceSteps:!1,substeps:!0,comment:!0}),o=`In a performance hall with $${y(s)}$ seats, the entry price for an adult is $${I(t)}$ € and for a child it is $${I(a)}$ €.<br>`,o+=`Tonight's show took place in front of a full house and the revenue is $${I(r)}$ €.<br>`,o+="How many adults were there in the room?",i="Let $x$ be the number of adult places sold.<br>",i+=`As the $${y(s)}$ places have been sold, the number of children's places is: $${s}-x$.<br>`,i+="Calculating the recipe gives the following equation.<br>",c=`<br>So there were $${y($)}$ adults at the show.`,m="",g=`<br>Verification:<br>$${n.verifLeftSide.printExpression} = ${n.verifLeftSide.printResult}$`;break;case 11:e=f({a:"randomInt(50,100)",c:"(1-2*round(randomInt(0,2)))*randomInt(10,30)",b:"a+c",d:"d=2*a+b",test:"a+a>b and b>0"},{valueOf:!0}),s=e.a,t=e.b,a=e.c,r=e.d,o=`An isosceles triangle has perimeter $${r}$ mm.`,a>0?o+=`Its base is greater than the equal sides of $${a}$ mm.`:o+=`Its base is smaller than the equal sides of $${-a}$ mm.`,M([!0,!1])?(o+="<br>What is the measurement of its base"+(C.isAmc?", in mm":"")+" ? (The figure is not full size.)",i=`Let $x$ be the length of its base. The length of equal sides is: $x${q(-a)}$.<br>`,i+="Calculating the perimeter gives the following equation:<br>",l=`2*(x${q(-a)})+x=${r}`,c=`<br>The base of this isosceles triangle therefore measures $${t}$ mm.`,$=t):(o+="<br>What is the measure of its equal sides? (the figure is not in real size)",i=`Let $x$ be the length of one of the equal sides. The length of the base is: $x${q(a)}$.<br>`,i+="Calculating the perimeter gives the following equation:<br>",l=`2*x+x${q(a)} = ${r}`,c=`<br>The two equal sides of this isosceles triangle therefore measure $${s}$ mm.`,$=s),n=x(l,{reduceSteps:!1,substeps:!0,comment:!0,suppr1:!1}),a>0?m=this.triangleIsocele2():m=this.triangleIsocele1(),g=`<br>Verification:<br>$${n.verifLeftSide.printExpression} = ${n.verifLeftSide.printResult}$`,u=[" units[Lengths]",new S($,"mm"),""];break;case 12:e=e=f({a:"randomInt(5,40)",b:"randomInt(5,40)",c:"randomInt(41,100)",d:"a*b/(c-a)",test:"d>0 and (a*b)%abs(c-a)==0"},{valueOf:!0}),s=e.a,t=e.b,a=e.c,r=e.d,$=Math.round(r),l=`(x+${t})*${s}=x*${a}`,n=x(l,{reduceSteps:!1,substeps:!1,comment:!0}),m=this.figureThales(s,t,a,""),o="Consider the figure below which is not in full size where $[CD]$ and $[AB]$ are parallel.",o+=` $AB=${a}\\text{mm}$, $AC=${t}\\text{mm}$ and $CD=${s}\\text{mm}$.<br> Determine the length $OC$${C.isAmc?", in mm.":"."}`,i="In this Thales configuration, we have the following equality: $\\dfrac{OC}{OA}=\\dfrac{CD}{AB}$.<br>",i+="This equality is equivalent to the equality of cross products: $OC\\times AB = CD\\times OA$.<br>",i+="By replacing the lengths with the data in the statement and setting $x=OC$, we obtain the following equation:<br>",c=`<br>so $OA=${$}\\text{mm}$.<br>`,g=`<br>Verification:<br>On the one hand: $${n.verifLeftSide.printExpression} = ${n.verifLeftSide.printResult}$<br>On the other hand: $${n.verifRightSide.printExpression} = ${n.verifRightSide.printResult}$`,u=[" units[Lengths]",new S($,"mm"),""];break;case 13:e=e=f({a:"randomInt(5,40)",b:"randomInt(5,40)",c:"randomInt(41,100)",d:"a*b/(c-a)",test:"d>0 and (a*b)%abs(c-a)==0"},{valueOf:!0}),s=e.a,$=e.b,a=e.c,r=e.d,t=Math.round(r),l=`(x+${t})*${s} = ${t}*${a}`,n=x(l,{reduceSteps:!1,substeps:!1,comment:!0}),m=this.figureThales(s,"",a,t),o="Consider the figure below which is not in full size where $[CD]$ and $[AB]$ are parallel.",o+=` $AB=${a}\\text{mm}$, $OC=${t}\\text{mm}$ and $CD=${s}\\text{mm}$.<br> Determine the length $AC$${C.isAmc?", in mm.":"."}`,i="In this Thales configuration, we have the following equality: $\\dfrac{OA}{OC}=\\dfrac{AB}{CD}$.<br>",i+="This equality is equivalent to the equality of cross products: $CD\\times OA = OC\\times AB$.<br>",i+="By replacing the lengths with the data in the statement and setting $x=OC$, we obtain the following equation:<br>",c=`<br>so $CA=${$}\\text{mm}$.<br>`,g=`<br>Verification:<br>$${n.verifLeftSide.printExpression} = ${n.verifLeftSide.printResult}$`,u=[" units[Lengths]",new S($,"mm"),""];break}p=o+m+H(this,b,"width10 inline"+u[0],{texteApres:j(2)+u[2]}),A=i,A+=`$${n.equation}$`,A+="<br>Let's solve the equation:<br>",A+=n.texteCorr,A+=g,A+=c,C.isAmc&&(this.autoCorrection[b]={enonce:p+"ddddddd<br>",enonceAvant:!1,propositions:[{type:"AMCOpen",propositions:[{enonce:p+"<br>Equate the problem below and solve it.",statut:3,pointilles:!0}]},{type:"AMCNum",propositions:[{texte:"",statut:"",reponse:{texte:"Answer to the problem:",valeur:[$],param:{digits:Math.max(G($),2),signe:!0}}}]}]}),this.questionJamaisPosee(b,$,s,t,r)&&(this.listeQuestions.push(p),this.listeCorrections.push(A),u[0]===""?V(this,b,$,{formatInteractif:"calculation"}):V(this,b,u[1],{formatInteractif:"units"}),b++),v++}J(this)}}export{ae as amcReady,ne as amcType,oe as dateDeModifImportante,ie as dateDePublication,le as default,se as interactifReady,re as interactifType,he as ref,te as titre,$e as uuid};
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