2013 AMC 8 Problems/Problem 2: Difference between revisions

Latest revision as of 20:18, 9 October 2025

Problem

A sign at the fish market says, "50 $\%$ off, today only: half-pound packages for just \$3 per package." What is the regular price for a full pound of fish, in dollars?

$\textbf{(A)}\ 6 \qquad \textbf{(B)}\ 9 \qquad \textbf{(C)}\ 10 \qquad \textbf{(D)}\ 12 \qquad \textbf{(E)}\ 15$

Solution 1

50% off the price of half a pound of fish is \$3, so 100%, the regular price, of a half pound of fish is \$6. If half a pound of fish costs \$6, then a whole pound of fish is $\boxed{\textbf{(D)}\ 12}$ dollars.

Solution 2

Suppose a full pound at normal price costs $x$ dollars. Then, with the 50% off deal, the full pound would cost $x/2$ dollars. A half pound of this would cost $x/4$ dollars (including the 50% off). 50% off half a pound is 3, so we form the equation $x/4=3\Rightarrow x=\boxed{\textbf{(D)}\ 12}$ .

Video Solution

https://youtu.be/om14Kv2jCck ~savannahsolver

2013 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 1	Followed by Problem 3
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All AJHSME/AMC 8 Problems and Solutions

These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. Error creating thumbnail: Unable to save thumbnail to destination

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 ==Problem==
-A sign at the fish market says, "50% off, today only: half-pound packages for just \$3 per package." What is the regular price for a full pound of fish, in dollars?
+A sign at the fish market says, "50<math>\%</math> off, today only: half-pound packages for just \$3 per package." What is the regular price for a full pound of fish, in dollars?
 <math>\textbf{(A)}\ 6 \qquad \textbf{(B)}\ 9 \qquad \textbf{(C)}\ 10 \qquad \textbf{(D)}\ 12 \qquad \textbf{(E)}\ 15</math>
-==Solution==
+==Solution 1==
-The 50% off price of half a pound of fish is \$3, so the 100%, or the regular price, of a half pound of fish is \$6. Consequently, if half a pound of fish costs \$6, then a whole pound of fish is <math>\boxed{\textbf{(D)}\ 12}</math> dollars.
+% off the price of half a pound of fish is \$3, so 100%, the regular price, of a half pound of fish is \$6. If half a pound of fish costs \$6, then a whole pound of fish is <math>\boxed{\textbf{(D)}\ 12}</math> dollars.
 ==Solution 2==
-Let's say that a full pound at normal price costs <math>x</math> dollars. Then, we can say that with the 50% off deal, the full pound would cost <math>x/2</math> dollars. Taking a half pound of this would make the cost <math>x/4</math> dollars for the deal. We know from the problem that this value is <math>3</math>. We can form the equation <math>x/4 = 3</math>. Solving for <math>x</math>, we get <math>x=12</math>. The answer is <math>\boxed{\textbf{(D)}\ 12}</math>.
+Suppose a full pound at normal price costs <math>x</math> dollars. Then, with the 50% off deal, the full pound would cost <math>x/2</math> dollars. A half pound of this would cost <math>x/4</math> dollars (including the 50% off). 50% off half a pound is 3, so we form the equation <math>x/4=3\Rightarrow x=\boxed{\textbf{(D)}\ 12}</math>.
 ==Video Solution==

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