"The ratio of cats to dogs is 3:5. If there are 32 dogs
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A ratio is a way to compare two or more quantities. It tells us how much of one thing there is compared to another. For example, if we have 3 circles and 5 squares, we can express this comparison as a ratio: 3 to 5, or written with a colon, 3:5.
Now let's look at our specific problem. The ratio of cats to dogs is 3:5. This means that for every 3 cats, there are 5 dogs. We can visualize this by grouping 3 cat icons with 5 dog icons. This pattern will repeat in larger quantities.
To solve ratio problems systematically, we think in terms of parts. In our ratio 3:5, we have 3 parts representing cats and 5 parts representing dogs, making a total of 8 parts. Each part represents the same quantity, so we can find the value of one part and then calculate the quantities we need.
We're told there are 32 dogs. Since dogs represent 5 parts in our ratio, we can set up the equation: 5 parts equals 32 dogs. To find the value of one part, we divide both sides by 5. So one part equals 32 divided by 5, which is 6.4. This means each part represents 6.4 animals.
Now we can find the number of cats. Since cats represent 3 parts, and each part is 6.4 animals, we multiply 3 by 6.4 to get 19.2 cats. However, we can't actually have 0.2 of a cat in reality. This suggests our problem might be theoretical or we should consider rounding. Let's verify our answer to make sure our calculations are correct.
Let's verify our answer by checking if the ratio 19.2 to 32 simplifies to 3:5. We divide both sides by 32, giving us 0.6 to 1. To convert this to whole numbers, we multiply both sides by 5, resulting in 3 to 5. This confirms our answer is correct! To summarize the method: First, identify the ratio parts. Second, find the value of one part using the given information. Third, calculate the unknown quantity by multiplying the number of parts by the value of one part. Finally, verify your answer by checking if it simplifies back to the original ratio.