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
It means that if there are 4 cats in the store there are 5 dogs, if there are 8 cats (4×2) there then there will be 10 dogs (5×2)
To find the total number of cats and dogs in the pet store, we need to determine the number of cats and dogs separately.
Let's assume the number of dogs as 'x'. Since there are 4 more cats than dogs, the number of cats can be expressed as 'x + 4'.
Given that the ratio of cats to dogs is 12 to 9, we can set up the equation:
(x + 4) / x = 12 / 9
To solve this equation, we can cross-multiply:
9(x + 4) = 12x
Simplifying further:
9x + 36 = 12x
Subtracting 9x from both sides:
36 = 3x
Dividing both sides by 3:
x = 12
Now that we know the number of dogs is 12, we can calculate the number of cats:
Number of cats = x + 4 = 12 + 4 = 16
Therefore, the total number of cats and dogs in the pet store is 12 + 16 = 28.