Difference between revisions of "2018 AMC 10A Problems/Problem 6"
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==Solution== | ==Solution== | ||
| − | If <math>65\%</math> of the votes were likes, then <math>35\%</math> of the votes were dislikes. <math>65\%-35\%=30\%</math>, so <math>90</math> votes is <math>30\%</math> of the total number of votes. Doing quick arithmetic shows that the answer is <math>\boxed{\textbf{(B) } 300}</math> | + | If <math>65\%</math> of the votes were likes, then <math>35\%</math> of the votes were dislikes. <math>65\%-35\%=30\%</math>, so <math>90</math> votes is <math>30\%</math> of the total number of votes. Doing quick arithmetic shows that the answer is <math>\boxed{\textbf{(B) } 300}</math>. |
| − | Sangho | + | ==Alternate Solution== |
| + | Let's consider that Sangho has received 100 votes. This means he has received 65 upvotes and 35 downvotes. Part of these upvotes and downvotes cancel out, so Sangho is now left with a total of 30 upvotes, or a score increase of 30. In order for his score to be 90, Sangho must receive three sets of 100 votes. Therefore, the answer is <math>\boxed{\textbf{(B) } 300}</math>. | ||
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| + | -tryanotherangle | ||
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== See Also == | == See Also == | ||
{{AMC10 box|year=2018|ab=A|num-b=5|num-a=7}} | {{AMC10 box|year=2018|ab=A|num-b=5|num-a=7}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 14:35, 29 November 2019
Problem
Sangho uploaded a video to a website where viewers can vote that they like or dislike a video. Each video begins with a score of 0, and the score increases by 1 for each like vote and decreases by 1 for each dislike vote. At one point Sangho saw that his video had a score of 90, and that 
of the votes cast on his video were like votes. How many votes had been cast on Sangho's video at that point?
Solution
If of the votes were likes, then 
of the votes were dislikes. 
, so 
votes is 
of the total number of votes. Doing quick arithmetic shows that the answer is 
.
Alternate Solution
Let's consider that Sangho has received 100 votes. This means he has received 65 upvotes and 35 downvotes. Part of these upvotes and downvotes cancel out, so Sangho is now left with a total of 30 upvotes, or a score increase of 30. In order for his score to be 90, Sangho must receive three sets of 100 votes. Therefore, the answer is .
-tryanotherangle
See Also
| 2018 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 5 |
Followed by Problem 7 | |
| 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 AMC 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
