Difference between revisions of "2007 AMC 8 Problems/Problem 2"
(Created page with '== Problem == <math>650</math> students were surveyed about their pasta preferences. The choices were lasagna, manicotti, ravioli and spaghetti. The results of the survey are dis…') |
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<math>650</math> students were surveyed about their pasta preferences. The choices were lasagna, manicotti, ravioli and spaghetti. The results of the survey are displayed in the bar graph. What is the ratio of the number of students who preferred spaghetti to the number of students who preferred manicotti? | <math>650</math> students were surveyed about their pasta preferences. The choices were lasagna, manicotti, ravioli and spaghetti. The results of the survey are displayed in the bar graph. What is the ratio of the number of students who preferred spaghetti to the number of students who preferred manicotti? | ||
| − | < | + | <asy> |
| + | size(200); | ||
| + | defaultpen(linewidth(0.7)); | ||
| + | defaultpen(fontsize(8)); | ||
| + | draw(origin--(0,250)); | ||
| + | int i; | ||
| + | for(i=0; i<6; i=i+1) { | ||
| + | draw((0,50*i)--(5,50*i)); | ||
| + | } | ||
| + | filldraw((25,0)--(75,0)--(75,150)--(25,150)--cycle, gray, black); | ||
| + | filldraw((75,0)--(125,0)--(125,100)--(75,100)--cycle, gray, black); | ||
| + | filldraw((125,0)--(175,0)--(175,150)--(125,150)--cycle, gray, black); | ||
| + | filldraw((225,0)--(175,0)--(175,250)--(225,250)--cycle, gray, black); | ||
| + | label("$50$", (0,50), W); | ||
| + | label("$100$", (0,100), W); | ||
| + | label("$150$", (0,150), W); | ||
| + | label("$200$", (0,200), W); | ||
| + | label("$250$", (0,250), W); | ||
| + | label(rotate(90)*"Lasagna", (50,0), S); | ||
| + | label(rotate(90)*"Manicotti", (100,0), S); | ||
| + | label(rotate(90)*"Ravioli", (150,0), S); | ||
| + | label(rotate(90)*"Spaghetti", (200,0), S); | ||
| + | label(rotate(90)*"$\mbox{Number of People}$", (-40,140), W); | ||
| + | </asy> | ||
<math>\mathrm{(A)} \frac{2}{5} \qquad \mathrm{(B)} \frac{1}{2} \qquad \mathrm{(C)} \frac{5}{4} \qquad \mathrm{(D)} \frac{5}{3} \qquad \mathrm{(E)} \frac{5}{2}</math> | <math>\mathrm{(A)} \frac{2}{5} \qquad \mathrm{(B)} \frac{1}{2} \qquad \mathrm{(C)} \frac{5}{4} \qquad \mathrm{(D)} \frac{5}{3} \qquad \mathrm{(E)} \frac{5}{2}</math> | ||
| − | |||
| − | |||
== Solution == | == Solution == | ||
| − | The answer is \ | + | The answer is <math>\dfrac{\text{number of students who preferred spaghetti}}{\text{number of students who preferred manicotti}}</math> |
So, | So, | ||
| Line 20: | Line 41: | ||
<math>\frac{5}{2}</math> | <math>\frac{5}{2}</math> | ||
| − | The answer is <math>\boxed{E}</math> | + | The answer is <math> \boxed{\textbf{(E)}\ \dfrac{5}{2}} </math> |
| + | |||
| + | ==Video Solution by SpreadTheMathLove== | ||
| + | https://www.youtube.com/watch?v=omFpSGMWhFc | ||
| + | |||
| + | ==Video Solution by WhyMath== | ||
| + | https://youtu.be/rcxZpl44uP0 | ||
| + | |||
| + | ==See Also== | ||
| + | {{AMC8 box|year=2007|num-b=1|num-a=3}} | ||
| + | {{MAA Notice}} | ||
Latest revision as of 16:29, 28 October 2024
Contents
Problem
students were surveyed about their pasta preferences. The choices were lasagna, manicotti, ravioli and spaghetti. The results of the survey are displayed in the bar graph. What is the ratio of the number of students who preferred spaghetti to the number of students who preferred manicotti?
![[asy] size(200); defaultpen(linewidth(0.7)); defaultpen(fontsize(8)); draw(origin--(0,250)); int i; for(i=0; i<6; i=i+1) { draw((0,50*i)--(5,50*i)); } filldraw((25,0)--(75,0)--(75,150)--(25,150)--cycle, gray, black); filldraw((75,0)--(125,0)--(125,100)--(75,100)--cycle, gray, black); filldraw((125,0)--(175,0)--(175,150)--(125,150)--cycle, gray, black); filldraw((225,0)--(175,0)--(175,250)--(225,250)--cycle, gray, black); label("$50$", (0,50), W); label("$100$", (0,100), W); label("$150$", (0,150), W); label("$200$", (0,200), W); label("$250$", (0,250), W); label(rotate(90)*"Lasagna", (50,0), S); label(rotate(90)*"Manicotti", (100,0), S); label(rotate(90)*"Ravioli", (150,0), S); label(rotate(90)*"Spaghetti", (200,0), S); label(rotate(90)*"$\mbox{Number of People}$", (-40,140), W); [/asy]](http://latex.artofproblemsolving.com/f/e/c/fec3399a97d908194ebbb1e95eff24484c816a96.png)
Solution
The answer is 
So,
Simplify,
The answer is 
Video Solution by SpreadTheMathLove
https://www.youtube.com/watch?v=omFpSGMWhFc
Video Solution by WhyMath
See Also
| 2007 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 1 |
Followed by Problem 3 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
