An animal shelter has a total of 350 animals comprised of cats, dogs, and rabbits. if the number of rabbits is 5 less than one-half the number of cats, and there are 20 more cats than dogs, how many cats are at the shelter?

This is the concept of algebra, suppose that the number of cats is x;
number of cats will be x-20
number of rabbits will be 3/2x
thus the total number of animals will be:
x+(x-20)+3/2x=350
7/2x=350+20
7/2x=370
x=370*2/7
x=105.7=106
therefore we conclude that there we 106 cats in the shelter