Answer: 15 cats
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Step-by-step explanation:
The tape diagram is shown below.
"C" represents a sub-group of cats, and "D" represents a sub-group of dogs. Each sub-group has the same number of animals.
There are 3 copies of "C" and 5 copies of "D" to represent the ratio 3:5 of cats to dogs. For every 3 cats, there are 5 dogs.
We are told there are 25 dogs available for adoption. This consists of all five blocks of "D" combined. If each "D" is the same number of dogs, then there must be 25/5 = 5 dogs per "D" block. By extension, there are 5 cats per "C" block.
In short, each block has 5 animals.
3 blocks of C = 3*5 = 15 cats are available.
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Another approach:
C = number of cats available = unknown
D = number of dogs available = 25
C/D = 3/5
C/25 = 3/5
5C = 25*3 ... cross multiply
5C = 75
C = 75/5
C = 15 cats are available
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A third approach:
The ratio 3:5 scales up to 15:25 after multiplying both parts by 5. This is so the "5" in "3:5" becomes "25".
The ratio of cats to dogs of 15:25 reduces to 3:5 when you divide both parts by the GCF 5.
So this is another way to see how 15 cats are available.