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2005 AMC 12B Problems/Problem 1: Difference between revisions

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{{duplicate|[[2005 AMC 12B Problems|2005 AMC 12B #1]] and [[2005 AMC 10B Problems/Problem 1|2005 AMC 10B #1]]}}
== Problem ==
== Problem ==
A scout troop buys <math>1000</math> candy bars at a price of five for <math>2</math> dollars. They sell all the candy bars at the price of two for <math>1</math> dollar.  What was their profit, in dollars?
A scout troop buys <math>1000</math> candy bars at a price of five for <math>2</math> dollars. They sell all the candy bars at the price of two for <math>1</math> dollar.  What was their profit, in dollars?
Line 13: Line 14:
<cmath>
<cmath>
\begin{align*}
\begin{align*}
\mbox{Cash out} &= 1000 \cdot \frac25 = 400 \\
\mbox{Expenses} &= 1000 \cdot \frac25 = 400 \\
\mbox{Cash in}  &= 1000 \cdot \frac12 = 500 \\
\mbox{Revenue}  &= 1000 \cdot \frac12 = 500 \\
\mbox{Profit}  &= \mbox{Cash out} - \mbox{Cash in} = 500-400 = \boxed{100}.
\mbox{Profit}  &= \mbox{Revenue} - \mbox{Expenses} = 500-400 = \boxed{(A) \,100}.
\end{align*}
\end{align*}
</cmath>
</cmath>


== See also ==
== See also ==
* [[2005 AMC 12B Problems]]
{{AMC10 box|year=2005|ab=A|before=First question|num-a=2}}
{{AMC12 box|year=2005|ab=A|before=First question|num-a=2}}

Revision as of 15:02, 28 June 2011

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?

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

Solution

\begin{align*} \mbox{Expenses} &= 1000 \cdot \frac25 = 400 \\ \mbox{Revenue} &= 1000 \cdot \frac12 = 500 \\ \mbox{Profit} &= \mbox{Revenue} - \mbox{Expenses} = 500-400 = \boxed{(A) \,100}. \end{align*}

See also

2005 AMC 10A (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 12A (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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