An animal shelter has 90 animals. some are dogs and the rest are cats. there are 11 dogs for every four cats. how many cats are at the animal shelter? explain your reasoning.

Step-by-step explanation:

The equation that we are trying to solve is basically this one:

dogs + cats = 90

But there are too many unknowns.  We have only 1 equation, therefore, we can only have 1 unknown.  We are told that for every 11 dogs, there are 4 cats.  Let's figure out, then, the number of dogs per 1 cat.  We do this by dividing.

11/4 = 2.75  This means that for every 1 cat, there are 2.75 the number of dogs.  Now we have something we can work with.

cats: c

dogs: 2.75c

Check this so we know we are doing it right.  If we replace c with the number 4, and then multiply that by 2.75, we find that the number of dogs is 11 for every 4 cats.  So we can replace the dogs with 2.75c:

2.75c + c = 90 and

3.75c = 90 so

c = 24.  That means that there are 24 cats at the shelter (which is 24 too many, if you ask me).

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b

if you was gonna solve for a, a is a   < -12