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Proportions - The Animal Shelter










































Algebra - Proportions

The animal shelter placed a total of 35 animals last month.

For every 2 cats,3dogs found a new home.

How many dogs found new homes?

How many cats?

Comments for Proportions - The Animal Shelter

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Aug 27, 2012
Proportions
by: Staff


Answer:

Variables:

Cats = number of cats placed in a new home

Dogs = number of dogs placed in a new home



The ratio of the number of cats to the number of dogs is a proportional relationship.

This ratio can be expressed as follows:


(Homes for 2 cats) is to (homes for 3 dogs) AS (total number of homes for cats) is to (total number of homes for dogs).

2:3 AS Cats:Dogs

2:3 = Cats:Dogs

2/3 = Cats/Dogs



The first equation

Solve for the number of cats using the proportional ratio:

Cats/Dogs = 2/3


Solve for the variable “Cats”

Multiply each side of the equation by the variable “Dogs”

(Cats/Dogs) * Dogs = (2/3) * Dogs

Cats * (Dogs / Dogs) = (2/3) * Dogs

Cats * (1) = (2/3) * Dogs

Cats = (2/3) * Dogs



The second equation

The animal shelter found homes for a total of 35 cats and dogs.

Cats + dogs = 35


Solve for “Dogs”

Substitute “(2/3) * Dogs” for the variable Cats

Cats + Dogs = 35

(2/3) * Dogs + Dogs = 35


Solve for the variable “Dogs”

(2/3) * Dogs + Dogs = 35


Multiply each side of the equation by 3

3 * [(2/3) * Dogs + Dogs] = 3 * 35

3 * (2/3) * Dogs + 3 * Dogs = 3 * 35

2 * (3/3) * Dogs + 3 * Dogs = 3 * 35

2 * (1) * Dogs + 3 * Dogs = 3 * 35

2 * Dogs + 3 * Dogs = 3 * 35


Combine like terms

2 * Dogs + 3 * Dogs = 105

5 * Dogs = 105


Divide each side of the equation by 5

5 * Dogs / 5 = 105 / 5

Dogs * (5/ 5) = 105 / 5

Dogs * (1) = 105 / 5

Dogs = 105 / 5

Dogs = 21


Substitute 21 for the variable “Dogs” in the first equation

Cats = (2 / 3) * Dogs

Cats = (2 / 3) * 21

Cats = (2) * (21 / 3)

Cats = (2) * (7)

Cats = 14



final answer

Number of Dogs = 21

Number of Cats = 14




Thanks for writing.

Staff
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