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

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

Revision as of 21:33, 16 October 2020

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 $\boxed{\textbf{(E)}\ \text{MLS}}$.

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

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