Difference between revisions of "2005 AMC 12B Problems/Problem 1"
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+ | {{duplicate|[[2005 AMC 12B Problems|2005 AMC 12B #1]] and [[2005 AMC 10B Problems|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? | |
<math> | <math> | ||
− | \mathrm{(A)}\ | + | \mathrm{(A)}\ 100 \qquad |
− | \mathrm{(B)}\ | + | \mathrm{(B)}\ 200 \qquad |
− | \mathrm{(C)}\ | + | \mathrm{(C)}\ 300 \qquad |
− | \mathrm{(D)}\ | + | \mathrm{(D)}\ 400 \qquad |
− | \mathrm{(E)}\ | + | \mathrm{(E)}\ 500 |
</math> | </math> | ||
== Solution == | == Solution == | ||
− | < | + | <cmath> |
+ | \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*} | ||
+ | </cmath> | ||
+ | Note: Revenue is a gain. | ||
− | <math> | + | ==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>. | |
− | <math>\ | + | ~HyperVoid |
== See also == | == See also == | ||
− | + | {{AMC10 box|year=2005|ab=B|before=First question|num-a=2}} | |
+ | {{AMC12 box|year=2005|ab=B|before=First question|num-a=2}} | ||
+ | {{MAA Notice}} |
Latest revision as of 00:40, 28 November 2020
- 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 candy bars at a price of five for dollars. They sell all the candy bars at the price of two for dollar. What was their profit, in dollars?
Solution
Note: Revenue is a gain.
Solution 2 (Faster)
Note that the troop buys candy bars at a price of dollars and sells bars at a price of dollars. So the troop gains dollar for every bars. So therefore we divide . So our answer is . ~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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.