Algebra
posted by Anonymous on .
In a pet store there are 4 more cats than dogs and the ratio of cats to dogs is 12 to 9.What is the total number of cats and dogs in the pet store ?

Remark:
12 = 4 * 3
9 = 3 * 3
12 / 9 = 4 * 3 / ( 3 * 3 ) = 4 / 3
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C = number of cats
D = numbers of dog
C = D + 4
C / D = 12 / 9
C / D = 3 * 4 / ( 3 * 3 )
C / D = 4 / 3
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In a pet store there are 4 more cats than dogs.
That mean C = D + 4
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C / D = 4 / 3
( D + 4 ) / D = 4 / 3 Multiply both sides by 3
3 ( D + 4 ) / D = 4 * 3 / 3
( 3 D + 12 ) / D = 4 Multiply both sides by D
( 3 D + 12 ) * D / D = 4 D
3 D + 12 = 4 D Subtract 3 D to both sides
3 D + 12  3 D = 4 D  D
12 = D
D = 12
C = D + 4
C = 12 + 4 = 16
16 Cats and 12 dogs.
The ratio of cats to dogs:
C / D = 16 / 12 = 4 * 4 / ( 4 * 3 ) = 4 / 3