Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Difference between revisions of "2005 AMC 8 Problems/Problem 22"

m (→‎Problem)
m
 
(9 intermediate revisions by 6 users not shown)
Line 1: Line 1:
 
==Problem==
 
==Problem==
 
A company sells detergent in three different sized boxes: small (S), medium (M) and large (L). The medium size costs 50% more than the small size and contains 20% less detergent than the large size. The large size contains twice as much detergent as the small size and costs 30% more than the medium size. Rank the three sizes from best to worst buy.
 
A company sells detergent in three different sized boxes: small (S), medium (M) and large (L). The medium size costs 50% more than the small size and contains 20% less detergent than the large size. The large size contains twice as much detergent as the small size and costs 30% more than the medium size. Rank the three sizes from best to worst buy.
 +
 +
<math>\text{(A)}\, SML \qquad \text{(B)}\, LMS \qquad \text{(C)}\, MSL \qquad \text{(D)}\, LSM \qquad \text{(E)}\, MLS</math>
  
 
==Solution==
 
==Solution==
−
Suppose the small size costs <math>\textdollar 1</math> and the large size has <math>10</math> oz. The medium size then costs <math>\textdollar 1.50</math> and has <math>8</math> oz. The small size has <math>5</math> oz and the large size costs <math>\textdollar 1.95</math>. The small, medium, and large size cost respectively, <math>0.200, 0.188, 0.195</math> dollars per oz. The sizes from best to worst buy are <math>\boxed{\textbf{(E)}\ \text{MLS}}</math>.
+
Suppose the small size costs <math>\textdollar 1</math> and has <math>5</math> oz. The medium size then costs <math>\textdollar 1.50</math> and has <math>8</math> oz. The large size costs <math>\textdollar 1.95</math> and has 10 oz. The small, medium, and large size cost respectively, <math>0.200, 0.188, 0.195</math> dollars per oz. The sizes from best to worst buy are <math>\boxed{\textbf{(E)}\ \text{MLS}}</math>.
 +
 
 +
==Video Solution==
 +
 
 +
https://www.youtube.com/watch?v=65cfokoNyfA  ~David
  
 
==See Also==
 
==See Also==
 
{{AMC8 box|year=2005|num-b=21|num-a=23}}
 
{{AMC8 box|year=2005|num-b=21|num-a=23}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Latest revision as of 14:02, 25 November 2024

Problem

A company sells detergent in three different sized boxes: small (S), medium (M) and large (L). The medium size costs 50% more than the small size and contains 20% less detergent than the large size. The large size contains twice as much detergent as the small size and costs 30% more than the medium size. Rank the three sizes from best to worst buy.

$\text{(A)}\, SML \qquad \text{(B)}\, LMS \qquad \text{(C)}\, MSL \qquad \text{(D)}\, LSM \qquad \text{(E)}\, MLS$

Solution

Suppose the small size costs $\textdollar 1$ and has $5$ oz. The medium size then costs $\textdollar 1.50$ and has $8$ oz. The large size costs $\textdollar 1.95$ and has 10 oz. The small, medium, and large size cost respectively, $0.200, 0.188, 0.195$ dollars per oz. The sizes from best to worst buy are $\boxed{\textbf{(E)}\ \text{MLS}}$.

Video Solution

https://www.youtube.com/watch?v=65cfokoNyfA ~David

See Also

2005 AMC 8 (Problems • Answer Key • Resources)
Preceded by
Problem 21 		Followed by
Problem 23
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. AMC logo.png

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2005_AMC_8_Problems/Problem_22&oldid=235573"