Question

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Answer 1

Given:

Total number of animals = 300

Number of rabbits is 10 less than one-half the number of cats

There are 25 more cats than dogs.

Let's find the number of each type of animal.

Let c represent the number of cats.

Let r represent the number of rabbits.

Let d represent the number of dogs.

Number of rabbits is 10 less than one-half the number of cats. This is expressed algebraically as:

r = 0.5c - 10

There are 25 more cats than dogs. This is expressed as:

d = c - 25

Hence, we have the equation:

c + (0.5c - 10) + (c - 25) = 300

Let's solve for c in the equtaion.

Remove the parentheses:

c + 0.5c - 10 + c - 25 = 300

• Combine like terms:

c + c + 0.5c - 10 - 25 = 300

2.5c - 35 = 300

• Add 35 to both sides:

2.5c - 35 + 35 = 300 + 35

2.5c = 335

• Divide both sides by 2.5:

`\begin{gathered} (2.5c)/(2.5)=(335)/(2.5) \\ \\ c=134 \end{gathered}`

Therefore, there are 134 cats.

• To find the number of rabbits, substitute 134 for c in (0.5c - 10).

Thus, we have:

r = 0.5c - 10

r = 0.5(134) - 10

r = 67 - 10

r = 57

Therefore, the number of rabbits is 57.

To find the number of dogs, substitute 134 for c in (c - 25).

Thus, we have:

d = c - 25

d = 134 - 25

d = 109

Therefore, there are 109 dogs.

ANSWER:

Number of cats, c = 134

Number of dogs, d = 109

Number of rabbits, r = 57