Westonci.ca offers fast, accurate answers to your questions. Join our community and get the insights you need now. Connect with a community of experts ready to provide precise solutions to your questions quickly and accurately. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.
Sagot :
Given the initial ratio of cats to dogs is 2:5 and there are 10 cats, we can find the number of dogs:
\[
\text{Let } C \text{ be the number of cats and } D \text{ be the number of dogs.}
\]
\[
C = 10 \text{ cats}
\]
Since the ratio of cats to dogs is 2:5, we can set up the following proportion:
\[
\frac{C}{D} = \frac{2}{5}
\]
Substituting \( C = 10 \):
\[
\frac{10}{D} = \frac{2}{5}
\]
Cross-multiplying to solve for \( D \):
\[
10 \times 5 = 2 \times D \implies 50 = 2D \implies D = \frac{50}{2} = 25
\]
So, initially, there are 10 cats and 25 dogs.
After a group of animals arrives, the new ratio of cats to dogs becomes 5:3. Let the number of new cats be \( x \) and the number of new dogs be \( y \). The new number of cats and dogs are:
\[
10 + x \text{ cats and } 25 + y \text{ dogs}
\]
According to the new ratio:
\[
\frac{10 + x}{25 + y} = \frac{5}{3}
\]
Cross-multiplying to solve for \( x \) and \( y \):
\[
3(10 + x) = 5
\[
\text{Let } C \text{ be the number of cats and } D \text{ be the number of dogs.}
\]
\[
C = 10 \text{ cats}
\]
Since the ratio of cats to dogs is 2:5, we can set up the following proportion:
\[
\frac{C}{D} = \frac{2}{5}
\]
Substituting \( C = 10 \):
\[
\frac{10}{D} = \frac{2}{5}
\]
Cross-multiplying to solve for \( D \):
\[
10 \times 5 = 2 \times D \implies 50 = 2D \implies D = \frac{50}{2} = 25
\]
So, initially, there are 10 cats and 25 dogs.
After a group of animals arrives, the new ratio of cats to dogs becomes 5:3. Let the number of new cats be \( x \) and the number of new dogs be \( y \). The new number of cats and dogs are:
\[
10 + x \text{ cats and } 25 + y \text{ dogs}
\]
According to the new ratio:
\[
\frac{10 + x}{25 + y} = \frac{5}{3}
\]
Cross-multiplying to solve for \( x \) and \( y \):
\[
3(10 + x) = 5
We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.
