Difference between revisions of "2008 AMC 8 Problems/Problem 9"
MRENTHUSIASM (talk | contribs) m (Undo revision 159790 by Raina0708 (talk) I messaged Raina0708 for the use of LaTeX. Deletion should not have been made.) (Tag: Undo) |
|||
| (4 intermediate revisions by 4 users not shown) | |||
| Line 1: | Line 1: | ||
==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 | ||
| Line 11: | Line 11: | ||
\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}} | ||
Latest revision as of 18:21, 8 August 2021
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. 
