Difference between revisions of "2019 AMC 8 Problems/Problem 22"
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==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 <math> | + | 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>\framebox{E}</math> |
==See Also== | ==See Also== |
Revision as of 20:26, 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 $40%$ (Error compiling LaTeX. Unknown error_msg), or
See Also
2019 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 6 |
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 |
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