Bunuel wrote:
A post on a website gains a point if a user choose to upvote it and loses a point if a user chooses to downvote it. If a post has a total of 60 points and 40% of the votes were downvotes, how many votes have been cast, in total?
A. 100
B. 150
C. 240
D. 300
E. 500
Let u = the number of upvotes and d = the number of downvotes. We can create the equations:
u - d = 60
and
d = 0.4(u + d)
Simplifying the second equation, we have:
d = 0.4u + 0.4d
0.6d = 0.4u
6d = 4u
1.5d = u
Now we can substitute 1.5d for u into the first equation and obtain:
1.5d - d = 60
0.5d = 60
d = 120
Since d = 120, u = 1.5 x 120 = 180. Therefore, a total of 180 + 120 = 300 votes have been cast.
Alternate Solution:
We can test each answer choice:
A) 100 total votes
If 100 votes were cast and 40% were downvotes, then there are 100*(0.4) = 40 downvotes and 100 - 40 = 60 upvotes. In this case, the post would have 60 - 40 = 20 total points. We can eliminate answer choice A.
B) 150 total votes
If 150 votes were cast and 40% were downvotes, then there are 150*(0.4) = 60 downvotes and 150 - 60 = 90 upvotes. In this case, the post would have 90 - 60 = 30 total points. We can eliminate answer choice B.
C) 240 total votes
If 240 votes were cast and 40% were downvotes, then there are 240*(0.4) = 96 downvotes and 240 - 96 = 144 upvotes. In this case, the post would have 144 - 96 = 48 total points. We can eliminate answer choice C.
D) 300 total votes
If 300 votes were cast and 40% were downvotes, then there are 300*(0.4) = 120 downvotes and 300 - 120 = 180 upvotes. In this case, the post would have 180 - 120 = 60 total points, as required. The answer is D.
Answer: D
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