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 x be the number of collies. Let 2x be the number of retrievers. Let x+2 be the number of shepards.

set x+2x+x+2=21 and solve

Answer 2

you're going to get a fraction, but make sure to round down because you can't have part of a dog

Answer 3

i need it to be an inequality so how would i do that??

Answer 4

ok, so the total number of dogs (the left hand side of the equation) needs to be less than or equal to 21 (the right hand side of the equation)

do you know the greater than or equal to symbol?

Answer 5

or the less than or equal to symbol?

Answer 6

Yea i do

Answer 7

ok, so the number of dogs has to be less than or equal to 21. insert the proper symbol where I put the = sign and tell me what you think it is

Answer 8

so is the answer x is greater than or equal to -9.5 or -19/2?

Answer 9

\[x+2x+x+2 \le 21\]

Answer 10

Ok, let's take a step back, I think you just made an arithmetic mistake

Answer 11

is it x is less than 19/4?

Answer 12

Yes perfect! Now what would that decimal be?

Answer 13

*less than or equal to

Answer 14

4.75?

Answer 15

Ok, so we can have \[x \le 4.75\]

Answer 16

but there cannot be .75 of a dog. So we have to round down

Answer 17

so then its just 4?

Answer 18

Correct. So 4 is our x value and x is our number of Collies. Therefore 4 is the maximum number of Collies that can be boarded. Does this make sense?

Answer 19

yes it does thank you

Answer 20

You're welcome :)