# 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

 Aug 27, 2012 Proportions by: Staff Answer:Variables:Cats = number of cats placed in a new homeDogs = number of dogs placed in a new homeThe 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:Dogs2:3 = Cats:Dogs2/3 = Cats/DogsThe first equationSolve for the number of cats using the proportional ratio:Cats/Dogs = 2/3Solve for the variable “Cats”Multiply each side of the equation by the variable “Dogs”(Cats/Dogs) * Dogs = (2/3) * DogsCats * (Dogs / Dogs) = (2/3) * DogsCats * (1) = (2/3) * DogsCats = (2/3) * Dogs The second equationThe animal shelter found homes for a total of 35 cats and dogs. Cats + dogs = 35Solve for “Dogs”Substitute “(2/3) * Dogs” for the variable CatsCats + Dogs = 35(2/3) * Dogs + Dogs = 35Solve for the variable “Dogs”(2/3) * Dogs + Dogs = 35Multiply each side of the equation by 33 * [(2/3) * Dogs + Dogs] = 3 * 353 * (2/3) * Dogs + 3 * Dogs = 3 * 352 * (3/3) * Dogs + 3 * Dogs = 3 * 352 * (1) * Dogs + 3 * Dogs = 3 * 352 * Dogs + 3 * Dogs = 3 * 35Combine like terms2 * Dogs + 3 * Dogs = 1055 * Dogs = 105Divide each side of the equation by 55 * Dogs / 5 = 105 / 5Dogs * (5/ 5) = 105 / 5Dogs * (1) = 105 / 5Dogs = 105 / 5Dogs = 21Substitute 21 for the variable “Dogs” in the first equation Cats = (2 / 3) * DogsCats = (2 / 3) * 21Cats = (2) * (21 / 3)Cats = (2) * (7)Cats = 14final answerNumber of Dogs = 21 Number of Cats = 14Thanks for writing. Staff www.solving-math-problems.com