At a local beach, the ratio of little dogs to average dogs to enormous dogs is 3:4:8.
At a local beach, the ratio of little dogs to average dogs to enormous dogs is 3:4:8. Late in the afternoon, the ratio of little dogs to average dogs doubles and the ratio of little dogs to enormous dogs increases. If the new percentage of little dogs and the new percentage of average dogs are both integers and there are fewer than 30 total dogs at the beach, which of the following represents a possible new percentage of enormous dogs?
Answer/Solution
50%
Steps/Work
Little Dogs(L), Average Dogs(A) and Enormous Dogs (E)
The initial ratio for L:A:E :: 3:4:8
Initial Total dogs = 15X ( x assumed; 2+5+8= 15), Since the total dogs are less than 30 therefore initial total value has to be 15
L = 3, A = 4 E = 8
L:A= 3:4
This ratio doubles
Hence New Dog count is
L= 6 , A = 4 E= X: Also 6+4+x<30
We need to Find X*100/(4+6+X)
Now it says that new percentage of little dogs and Average dogs is an integer
%L = 6*100/(10+x) %A = 4*100/(10+x); Only Value for X is 10 ; 9+x<30 and % integer
Therefore, Enormus Dogs % is = 10*100/(20) = 50%
D
The initial ratio for L:A:E :: 3:4:8
Initial Total dogs = 15X ( x assumed; 2+5+8= 15), Since the total dogs are less than 30 therefore initial total value has to be 15
L = 3, A = 4 E = 8
L:A= 3:4
This ratio doubles
Hence New Dog count is
L= 6 , A = 4 E= X: Also 6+4+x<30
We need to Find X*100/(4+6+X)
Now it says that new percentage of little dogs and Average dogs is an integer
%L = 6*100/(10+x) %A = 4*100/(10+x); Only Value for X is 10 ; 9+x<30 and % integer
Therefore, Enormus Dogs % is = 10*100/(20) = 50%
D