Difference between revisions of "2019 AMC 8 Problems/Problem 22"
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==Problem 22== | ==Problem 22== | ||
| − | A store increased the original price of a shirt by a certain percent and then decreased the new | + | 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 <math>84\%</math> of the original price, by what percent was the price increased and decreased? |
| − | 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? | ||
<math>\textbf{(A) }16\qquad\textbf{(B) }20\qquad\textbf{(C) }28\qquad\textbf{(D) }36\qquad\textbf{(E) }40</math> | <math>\textbf{(A) }16\qquad\textbf{(B) }20\qquad\textbf{(C) }28\qquad\textbf{(D) }36\qquad\textbf{(E) }40</math> | ||
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==Solution 1== | ==Solution 1== | ||
Revision as of 11:06, 22 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 
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. 
