Difference between revisions of "2020 AMC 8 Problems/Problem 15"
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Letting <math>x=100</math>, our equation becomes <math>0.15\cdot 100 = 0.2\cdot y \implies 15 = \frac{y}{5} \implies y=75</math>. Clearly, <math>y</math> is <math>75\%</math> of <math>x</math> and the answer is <math>\boxed{\textbf{C}}</math>.<br> | Letting <math>x=100</math>, our equation becomes <math>0.15\cdot 100 = 0.2\cdot y \implies 15 = \frac{y}{5} \implies y=75</math>. Clearly, <math>y</math> is <math>75\%</math> of <math>x</math> and the answer is <math>\boxed{\textbf{C}}</math>.<br> | ||
~ junaidmansuri | ~ junaidmansuri | ||
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| + | ==Solution 3== | ||
| + | Let us transform the first sentence to an equation. <math>15\%=\frac3{20}</math> and <math>20\%=\frac15.</math> So, <math>\frac3{20}x=\frac15y.</math> Therefore, <math>\frac1{20}x=\frac1{15}y</math> and <math>x=\frac43y,</math> hence <math>\boxed{\textbf{(C) }75}</math>. | ||
==See also== | ==See also== | ||
{{AMC8 box|year=2020|num-b=14|num-a=16}} | {{AMC8 box|year=2020|num-b=14|num-a=16}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 07:40, 18 November 2020
Suppose 
of 
equals 
of 
What percentage of is 
Contents
Solution 1
Multiply by 
to get 
. The 
here can be converted to 
. Therefore, 
is the answer.
Solution 2
Letting 
, our equation becomes 
. Clearly, 
is of and the answer is .
~ junaidmansuri
Solution 3
Let us transform the first sentence to an equation. 
and 
So, 
Therefore, 
and 
hence 
.
See also
| 2020 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 14 |
Followed by Problem 16 | |
| 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. 
