2005 AMC 8 Problems/Problem 22

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 the large size has $10$ oz. The medium size then costs $\textdollar 1.50$ and has $8$ oz. The small size has $5$ oz and the large size costs $\textdollar 1.95$ . 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 $\boxed{\textbf{(E)}\ \text{MLS}}$ .

Solution 2

This problem is not really direct, so lets define variables. Let $x$ be the amount of detergent in S, and $a$ be the prize of S. Then we have, $2x=$ the amount of detergent L, and $1.6x=$ the amount of detergent in M.

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.

Page

Toolbox

Search

2005 AMC 8 Problems/Problem 22

Contents

Problem

Solution

Solution 2

See Also