SOLUTION: there were 200 dogs in an compound, 99% of which were brown, how many brown dogs must be removed to make the percentage of brown dogs 98%??

Question 1069914: there were 200 dogs in an compound, 99% of which were brown, how many brown dogs must be removed to make the percentage of brown dogs 98%??
Found 3 solutions by josgarithmetic, Theo, ikleyn:
Answer by josgarithmetic(39630)   (Show Source): You can put this solution on YOUR website!
ONLY removing n of the brown dogs? This also removes reduces the total amount of remaining dogs.

n=100

-
CHECK:

Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
there are 200 dogs in the compound.
99% of them are brown.
that means there are 198 brown dogs and 2 dogs that are not brown.

let x equal the number of brown dogs that are removed.

if you remove x brown dogs, then you are also removing x dogs from the total.

i believe your formula should be:

198 - x = .98 * (200 - x).

simplify this to get 198 - x = 196 - .98 * x

subtract 196 from both sides of this equation and add x to both sides of this equation to get:

2 = .02 * x

divide both sides of this equation by .02 to get:

2/.02 = x

solve for x to get x 2/.02 = 200/2 = 100.

you would have to remove 100 dogs to make the percent equal to 98.

198 - 100 = 98.

200 - 100 = 100

98/100 = .98 * 100 = 98%.

as strange as it sounds, you would have to remove 100 brown dogs to make the percentage of brown dogs equal to 98%.

this is because, every time you remove a brown dog, the total number of dogs is reduced by 1.

to see if this makes sense, try some numbers less than 100.

if you remove 2 brown dogs, then you have 196 out of a total of 198.
the percentage is 98.9.....
if you remove 50 brown dogs, then you have 148 out of a total of 150.
the percentage is 98.67.

if you remove 100 brown dogs, then you have 98 / 100 = 98%.

note that the number of dogs that are not brown never changes.

you still have 2 dogs that are not brown.

2 / 100 = .02 = 2%.

this means that the percent of brown dogs is 98%.

Answer by ikleyn(52914)   (Show Source): You can put this solution on YOUR website!
.
Same feature as in the lesson
    - Problems on percentage that lead to unexpected results
in this site.

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