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Difference between revisions of "2005 AMC 12B Problems/Problem 1"

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<math>
 
<math>
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\mathrm{(A)}\ 100      \qquad
+
\textbf{(A) }\ 100      \qquad
−
\mathrm{(B)}\ 200      \qquad
+
\textbf{(B) }\ 200      \qquad
−
\mathrm{(C)}\ 300      \qquad
+
\textbf{(C) }\ 300      \qquad
−
\mathrm{(D)}\ 400      \qquad
+
\textbf{(D) }\ 400      \qquad
−
\mathrm{(E)}\ 500
+
\textbf{(E) }\ 500
 
</math>
 
</math>
  
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\mbox{Expenses} &= 1000 \cdot \frac25 = 400 \\
 
\mbox{Expenses} &= 1000 \cdot \frac25 = 400 \\
 
\mbox{Revenue}  &= 1000 \cdot \frac12 = 500 \\
 
\mbox{Revenue}  &= 1000 \cdot \frac12 = 500 \\
−
\mbox{Profit}  &= \mbox{Revenue} - \mbox{Expenses} = 500-400 = \boxed{(A) \,100}.
+
\mbox{Profit}  &= \mbox{Revenue} - \mbox{Expenses} = 500-400 = \boxed{\textbf{(A) }100}.
 
\end{align*}
 
\end{align*}
 
</cmath>
 
</cmath>
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==Solution 2 (Faster)==
 
==Solution 2 (Faster)==
−
Note that the troop buys <math>10</math> candy bars at a price of <math>4</math> dollars and sells <math>10</math> bars at a price of <math>5</math> dollars. So the troop gains <math>1</math> dollar for every <math>10</math> bars. So therefore we divide <math>1,000 \div 10 = 100</math>. So our answer is <math>\boxed{\mathrm{(A)}\ 100}</math>.
+
Note that the troop buys <math>10</math> candy bars at a price of <math>4</math> dollars and sells <math>10</math> bars at a price of <math>5</math> dollars. So the troop gains <math>1</math> dollar for every <math>10</math> bars. So therefore we divide <math>1000 \div 10 = 100</math>. So our answer is <math>\boxed{\textbf{(A) }100}</math>.
 
~HyperVoid
 
~HyperVoid
  

Latest revision as of 12:53, 14 December 2021

The following problem is from both the 2005 AMC 12B #1 and 2005 AMC 10B #1, so both problems redirect to this page.

Problem

A scout troop buys $1000$ candy bars at a price of five for $2$ dollars. They sell all the candy bars at the price of two for $1$ dollar. What was their profit, in dollars?

$\textbf{(A) }\ 100 \qquad \textbf{(B) }\ 200 \qquad \textbf{(C) }\ 300 \qquad \textbf{(D) }\ 400 \qquad \textbf{(E) }\ 500$

Solution

\begin{align*} \mbox{Expenses} &= 1000 \cdot \frac25 = 400 \\ \mbox{Revenue} &= 1000 \cdot \frac12 = 500 \\ \mbox{Profit} &= \mbox{Revenue} - \mbox{Expenses} = 500-400 = \boxed{\textbf{(A) }100}. \end{align*} Note: Revenue is a gain.

Solution 2 (Faster)

Note that the troop buys $10$ candy bars at a price of $4$ dollars and sells $10$ bars at a price of $5$ dollars. So the troop gains $1$ dollar for every $10$ bars. So therefore we divide $1000 \div 10 = 100$. So our answer is $\boxed{\textbf{(A) }100}$. ~HyperVoid

See also

2005 AMC 10B (Problems • Answer Key • Resources)
Preceded by
First question 		Followed by
Problem 2
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 AMC 10 Problems and Solutions
2005 AMC 12B (Problems • Answer Key • Resources)
Preceded by
First question 		Followed by
Problem 2
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 AMC 12 Problems and Solutions

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