Difference between revisions of "2019 AMC 8 Problems/Problem 22"
(→Solution 1) |
(→Solution 1) |
||
| Line 7: | Line 7: | ||
==Solution 1== | ==Solution 1== | ||
| − | Suppose the amount of discount is <math>x</math>. That means <math>(1-x)(1+x)=0.84x</math>; so <math>1-x^{2}=0.84</math>, and <math>(x^{2})=0.16</math>, obtaining <math>x=0.4</math>. Therefore, the price was increased and decreased by 40%, or <math>\boxed{\textbf{(E)}\ 40 | + | Suppose the amount of discount is <math>x</math>. That means <math>(1-x)(1+x)=0.84x</math>; so <math>1-x^{2}=0.84</math>, and <math>(x^{2})=0.16</math>, obtaining <math>x=0.4</math>. Therefore, the price was increased and decreased by <math>40</math>%, or <math>\boxed{\textbf{(E)}\ 40}</math>. |
==See Also== | ==See Also== | ||
Revision as of 21:16, 20 November 2019
Problem 22
A store increased the original price of a shirt by a certain percent and then decreased the new
price by the same amount. Given that the resulting price was 84% of the original price, by what
percent was the price increased and decreased?
Solution 1
Suppose the amount of discount is 
. That means 
; so 
, and 
, obtaining 
. Therefore, the price was increased and decreased by 
%, or 
.
See Also
| 2019 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 21 |
Followed by Problem 23 | |
| 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. 
