SOLUTION: A certain pet store has only cats and dogs. The ratio of the number of cats to the number of dogs in the pet store is 2:3. 1/4 of the cats and 1/2 of the dogs wear collars. If ther

Algebra ->  Finance -> SOLUTION: A certain pet store has only cats and dogs. The ratio of the number of cats to the number of dogs in the pet store is 2:3. 1/4 of the cats and 1/2 of the dogs wear collars. If ther      Log On


   

Question 1036213: A certain pet store has only cats and dogs. The ratio of the number of cats to the number of dogs in the pet store is 2:3. 1/4 of the cats and 1/2 of the dogs wear collars. If there are 48 animals that wear collars, how many animals are in the pet store?
Found 2 solutions by rfer, josmiceli:
Answer by rfer(16322) About Me  (Show Source):
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +c+ = number of cats in pet store
Let +d+ = number of dogs in pet store
+c%2Fd+=+2%2F3+
(1) +c+=+%282%2F3%29%2Ad+
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+%281%2F4%29%2Ac+%2B+%281%2F2%29%2Ad+=+48+
multiply both sides by +4+
(2) +c+%2B+2d+=+192+
Substitute (1) into (2)
(2) +%282%2F3%29%2Ad+%2B+2d+=+192+
(2) +%288%2F3%29%2Ad+=+192+
(2) +8d+=+576+
(2) +d+=+72+
and
(1) +c+=+%282%2F3%29%2Ad+
(1) +c+=+%282%2F3%29%2A72+
(1) +c+=+48+
----------------------
+c+%2B+d+=+72+%2B+48+
+c+%2B+d+=+120+
120 animals are in the pet store
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check:
+%281%2F4%29%2Ac+%2B+%281%2F2%29%2Ad+=+48+
+%281%2F4%29%2A48+%2B+%281%2F2%29%2A72+=+48+
+12+%2B+36+=+48+
+48+=+48+
OK