Difference between revisions of "1986 AJHSME Problems/Problem 16"
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What we want to find is the number of hamburgers sold in the winter. Since we don't know what it is, let's call it <math>x</math>. From the graph, we know that in Spring, 4.5 million hamburgers were sold, in the Summer was 5 million and in the Fall was 4 million. We know that the number of hamburgers sold in Fall is exactly <math>\frac{1}{4}</math> of the total number of hamburgers sold, so we can say that... | What we want to find is the number of hamburgers sold in the winter. Since we don't know what it is, let's call it <math>x</math>. From the graph, we know that in Spring, 4.5 million hamburgers were sold, in the Summer was 5 million and in the Fall was 4 million. We know that the number of hamburgers sold in Fall is exactly <math>\frac{1}{4}</math> of the total number of hamburgers sold, so we can say that... | ||
| − | <math>4 \times Fall = Spring + Winter + Fall + Summer</math> | + | <math>4 \times \text{Fall} = \text{Spring} + \text{Winter} + \text{Fall} + \text{Summer}</math> |
<math>4 \times 4 = 4.5 + 4 + x + 5</math> | <math>4 \times 4 = 4.5 + 4 + x + 5</math> | ||
| Line 57: | Line 57: | ||
<math>2.5 = x</math> | <math>2.5 = x</math> | ||
| − | The answer is 2.5, or A | + | The answer is 2.5, or <math>\boxed{\text{A}}</math> |
==See Also== | ==See Also== | ||
[[1986 AJHSME Problems]] | [[1986 AJHSME Problems]] | ||
Revision as of 17:47, 24 January 2009
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 
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]](http://latex.artofproblemsolving.com/d/c/5/dc539dcb21d5e32b5308de73865c080db86be764.png)
Solution
What we want to find is the number of hamburgers sold in the winter. Since we don't know what it is, let's call it 
. From the graph, we know that in Spring, 4.5 million hamburgers were sold, in the Summer was 5 million and in the Fall was 4 million. We know that the number of hamburgers sold in Fall is exactly 
of the total number of hamburgers sold, so we can say that...
The answer is 2.5, or 
