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Question

Difficulty: EasyRatios, Rates, and Proportions

An animal shelter has a ratio of cats to dogs of 4:74:7. If there are 28 cats currently at the shelter, what is the total number of cats and dogs at the shelter?

  1. A
    16
  2. B
    39
  3. C
    44
  4. D
    49
  5. 77Answer

Answer

The correct answer is 77, representing the total number of cats and dogs at the shelter.
The ratio of cats to dogs is 4:7, which means for every 4 cats there are 7 dogs. Since there are 28 cats, we can find the scaling multiplier by dividing the number of cats by 4: 28 / 4 = 7. Applying this same scaling factor to the dogs gives 7 * 7 = 49 dogs. Adding the cats and dogs together gives a total of 28 + 49 = 77 animals.

Step-by-Step Solution

1
Determine the scale factor for the cats by dividing the number of cats by their ratio part.
28÷4=728 \div 4 = 7
To find out how many animals each unit in the ratio represents.
2
Calculate the number of dogs by multiplying the scale factor by the dogs' ratio part.
7×7=497 \times 7 = 49 dogs
Since the ratio of cats to dogs is 4:7, there are 7 dogs for every 4 cats.
3
Find the total number of animals by adding the number of cats and dogs.
28+49=7728 + 49 = 77
The question asks for the combined total of both cats and dogs.

Key Concept

Solving proportions using scaling factors to find a total quantity from a given ratio.

Alternative Method

Find the total number of parts in the ratio (4 + 7 = 11 parts). Since 4 parts represent 28 cats, each part represents 28 / 4 = 7 animals. Therefore, the total number of animals is 11 parts * 7 animals/part = 77.
Estimated Time:1m 0s
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Topics

Ratios, Rates, and Proportions

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