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A certain dog kennel houses only collies, labs, and golden
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14 Jun 2018, 14:20
14 Jun 2018, 14:20
Expert Reply
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Question Stats:
85% (01:51) correct
14% (02:45) wrong based on 56 sessions
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A certain dog kennel houses only collies, labs, and golden retrievers. If the ratio of collies to labs is 5 : 9, there are 66 golden retrievers, and 12 more golden retrievers than labs in the kennel, what percent of the dogs in the kennel are collies?
(A) 5%
(B) 9%
(C) 12%
(D) 20%
(E) 25%
(A) 5%
(B) 9%
(C) 12%
(D) 20%
(E) 25%
Re: A certain dog kennel houses only collies, labs, and golden
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15 Jun 2018, 07:54
15 Jun 2018, 07:54
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sandy wrote:
A certain dog kennel houses only collies, labs, and golden retrievers. If the ratio of collies to labs is 5 : 9, there are 66 golden retrievers, and 12 more golden retrievers than labs in the kennel, what percent of the dogs in the kennel are collies?
(A) 5%
(B) 9%
(C) 12%
(D) 20%
(E) 25%
(A) 5%
(B) 9%
(C) 12%
(D) 20%
(E) 25%
I took 3:34 secs for this question
collies : labs : golden retrievers => c:l:g
Given that c/l = 5x/9x --> eq 1
Given total g = 66 and now question say that golden retrievers are 12 more than labs i.e. l = 54.
From eq 1 , we can take 9x = 54, x = 6
then c = 30.
Now c/c+l+g = 30/150 => 0.2.
D.
Re: A certain dog kennel houses only collies, labs, and golden
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05 Jul 2018, 03:02
05 Jul 2018, 03:02
Expert Reply
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Explanation
Start by assigning variables:
C = Number of collies
L = Number of labs
G = Number of golden retrievers
According to the given information:
G = 66
L = 66 – 12
L = 54
Ratios work like fractions, and you can set them up accordingly:
\(\frac{5}{9}=\frac{C}{54}\)
Cross-multiplying and simplifying, you get:
C = 30
Now take the number of collies and express it as a percent of the total number of dogs:
Total # of Dogs = 30 + 54 + 66 = 150
\(\frac{30}{150}*100=20%\)
Start by assigning variables:
C = Number of collies
L = Number of labs
G = Number of golden retrievers
According to the given information:
G = 66
L = 66 – 12
L = 54
Ratios work like fractions, and you can set them up accordingly:
\(\frac{5}{9}=\frac{C}{54}\)
Cross-multiplying and simplifying, you get:
C = 30
Now take the number of collies and express it as a percent of the total number of dogs:
Total # of Dogs = 30 + 54 + 66 = 150
\(\frac{30}{150}*100=20%\)
