Question

At Cheryl's Canine Resort, there are reservations for twice as many retrievers as collies, and for two more shepards than collies. If there are 21 cages in all, what is the greatest number of collies that can be boarded

Answer 1

let collies = x
"twice as many retrievers as collies" so retrievers = 2x
"two more shepards than colllies" so shepards = x + 2

so adding them all up gives us

x + 2x + (x+2) = 21
solve for x, and if necessary, round down to the nearest whole #, since we are talking about dogs, we can't have fractions/decimals
if we round up, that would cause us to exceed the # of available slots