Difference between revisions of "2007 AMC 8 Problems/Problem 2"
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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> | ||
| Line 8: | Line 31: | ||
== 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 18: | 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> |
| + | |||
==See Also== | ==See Also== | ||
{{AMC8 box|year=2007|num-b=1|num-a=3}} | {{AMC8 box|year=2007|num-b=1|num-a=3}} | ||
| + | {{MAA Notice}} | ||
Latest revision as of 12:21, 12 July 2021
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 
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. 
