Difference between revisions of "2008 AMC 8 Problems/Problem 9"
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| − | ==Problem | + | ==Problem== |
| − | In <math>2005</math> Tycoon Tammy invested <math>100</math> dollars for two years. During | + | In <math>2005</math> Tycoon Tammy invested <math>100</math> dollars for two years. During the first year |
her investment suffered a <math>15\%</math> loss, but during the second year the remaining | her investment suffered a <math>15\%</math> loss, but during the second year the remaining | ||
investment showed a <math>20\%</math> gain. Over the two-year period, what was the change | investment showed a <math>20\%</math> gain. Over the two-year period, what was the change | ||
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\textbf{(E)}\ 5\%\text{ gain}</math> | \textbf{(E)}\ 5\%\text{ gain}</math> | ||
| + | ==Solution== | ||
| + | After the <math>15 \%</math> loss, Tammy has <math>100 \cdot 0.85 = 85</math> dollars. After the <math>20 \%</math> gain, she has <math>85 \cdot 1.2 = 102</math> dollars. This is an increase in <math>2</math> dollars from her original <math>100</math> dollars, a <math>\boxed{\textbf{(D)}\ 2 \%\ \text{gain}}</math>. | ||
==See Also== | ==See Also== | ||
{{AMC8 box|year=2008|num-b=8|num-a=10}} | {{AMC8 box|year=2008|num-b=8|num-a=10}} | ||
| + | {{MAA Notice}} | ||
Revision as of 20:51, 7 February 2018
Problem
In 
Tycoon Tammy invested 
dollars for two years. During the first year
her investment suffered a 
loss, but during the second year the remaining
investment showed a 
gain. Over the two-year period, what was the change
in Tammy's investment?
Solution
After the 
loss, Tammy has 
dollars. After the 
gain, she has 
dollars. This is an increase in 
dollars from her original dollars, a 
.
See Also
| 2008 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 8 |
Followed by Problem 10 | |
| 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 AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
