Difference between revisions of "2009 AMC 10B Problems/Problem 8"
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<cmath>x = 100 \cdot \frac{0.2p}{1.2p} = \frac {100}{6} \approx 16.7.</cmath> | <cmath>x = 100 \cdot \frac{0.2p}{1.2p} = \frac {100}{6} \approx 16.7.</cmath> | ||
So to the nearest integer <math>x</math> is <math>\boxed{17}</math>. The answer is <math>\mathrm{(B)}</math>. | So to the nearest integer <math>x</math> is <math>\boxed{17}</math>. The answer is <math>\mathrm{(B)}</math>. | ||
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| + | == Solution 2 == | ||
| + | Without loss of generality, we can assume the price at the beginning of January was <math>100</math>. When it rose by <math>20%</math>, it became <math>120</math>, when it fell by <math>20</math>, it became <math>96</math>, and when it rose by <math>25%</math>, it became <math></math> | ||
== See also == | == See also == | ||
Revision as of 17:01, 14 June 2023
- The following problem is from both the 2009 AMC 10B #8 and 2009 AMC 12B #7, so both problems redirect to this page.
Contents
Problem
In a certain year the price of gasoline rose by 
during January, fell by during February, rose by 
during March, and fell by 
during April. The price of gasoline at the end of April was the same as it had been at the beginning of January. To the nearest integer, what is 
Solution
Let 
be the price at the beginning of January. The price at the end of March was 
Because the price at the end of April was , the price decreased by 
during April, and the percent decrease was
![\[x = 100 \cdot \frac{0.2p}{1.2p} = \frac {100}{6} \approx 16.7.\]](http://latex.artofproblemsolving.com/f/7/a/f7a133f61c84005792fb54e3b863469ff7dc7de6.png)
So to the nearest integer is 
. The answer is 
.
Solution 2
Without loss of generality, we can assume the price at the beginning of January was 
. When it rose by $20%$ (Error compiling LaTeX. Unknown error_msg), it became 
, when it fell by 
, it became 
, and when it rose by $25%$ (Error compiling LaTeX. Unknown error_msg), it became $$ (Error compiling LaTeX. Unknown error_msg)
See also
| 2009 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 7 |
Followed by Problem 9 | |
| 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 | ||
| 2009 AMC 12B (Problems • Answer Key • Resources) | |
| Preceded by Problem 6 |
Followed by Problem 8 |
| 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. 
