Art of Problem Solving

1986 AJHSME Problems/Problem 17: Difference between revisions

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New page: ==Problem== A bar graph shows the number of hamburgers sold by a fast food chain each season. However, the bar indicating the number sold during the winter is covered by a smudge. If ex...
 
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==Problem==


A bar graph shows the number of hamburgers sold by a fast food chain each season.  However, the bar indicating the number sold during the winter is covered by a smudge.  If exactly <math>25\% </math> of the chain's hamburgers are sold in the fall, how many million hamburgers are sold in the winter?
<asy>
size(250);
void bargraph(real X, real Y, real ymin, real ymax, real ystep, real tickwidth,
string yformat, Label LX, Label LY, Label[] LLX, real[] height,pen p=nullpen)
{
draw((0,0)--(0,Y),EndArrow);
draw((0,0)--(X,0),EndArrow);
label(LX,(X,0),plain.SE,fontsize(9));
label(LY,(0,Y),plain.NW,fontsize(9));
real yscale=Y/(ymax+ystep);
for(real y=ymin; y<ymax; y+=ystep)
{
draw((-tickwidth,yscale*y)--(0,yscale*y));
label(format(yformat,y),(-tickwidth,yscale*y),plain.W,fontsize(9));
}
int n=LLX.length;
real xscale=X/(2*n+2);
for(int i=0;i<n;++i)
{
real x=xscale*(2*i+1);
path P=(x,0)--(x,height[i]*yscale)--(x+xscale,height[i]*yscale)--(x+xscale,0)--cycle;
fill(P,p);
draw(P);
label(LLX[i],(x+xscale/2),plain.S,fontsize(10));
}
for(int i=0;i<n;++i) draw((0,height[i]*yscale)--(X,height[i]*yscale),dashed);
}
string yf="%#.1f";
Label[] LX={"Spring","Summer","Fall","Winter"};
for(int i=0;i<LX.length;++i) LX[i]=rotate(90)*LX[i];
real[] H={4.5,5,4,4};
bargraph(60,50,1,5.1,0.5,2,yf,"season","hamburgers (millions)",LX,H,yellow);
fill(ellipse((45,30),7,10),brown);
</asy>
<math>\text{(A)}\ 2.5 \qquad \text{(B)}\ 3 \qquad \text{(C)}\ 3.5 \qquad \text{(D)}\ 4 \qquad \text{(E)}\ 4.5</math>
==Solution==
{{Solution}}
==See Also==
[[1986 AJHSME Problems]]

Revision as of 19:43, 20 January 2009