Question

Dogs in the GoodDog Obedience School win a blue ribbon for learning how to sit, a green ribbon for learning how to roll over, and a white ribbon for learning how to stay. There are 100 dogs in the school.

73 have blue ribbons, 39 have green ribbons, and 62 have white ribbons.

21 have a blue ribbon and a green ribbon; 28 have a green ribbon and a white ribbon; 41 have a blue ribbon and a white ribbon.

14 have all three ribbons.

How many dogs have not learned any tricks?

Answer 1

let's start by drawing a venn diagram with three circles, one for blue one for white one for green, with the appropriate intersections marked

Answer 2

start with the center 14 since 14 dogs are known to have all three colors

Answer 3

then let's take a look at the middle paragraph

21 have a blue ribbon and a green ribbon; 28 have a green ribbon and a white ribbon; 41 have a blue ribbon and a white ribbon.

21 = blue + green. keep in mind this also includes the 14 dogs that have gotten all three ribbons, so blue + green only = 21 - 14 = 7

same logic with the others

28 = green + white
so 28 - 14 = 14 = green + white only

41 = blue + white
41 - 14 = 27 = blue + white only

let's mark these in the appropriate sections

Answer 4

then let's go back to the first paragraph

73 have blue ribbons, 39 have green ribbons, and 62 have white ribbons.

73 blue includes
- those who have blue only
- those who have blue + one other color
- those who have all three colors

so take 73, subtract the other two #'s we have in the blue circle

73 - 7 - 14 - 27 = 25 blue only

same logic w/ the other two circles green and white

green only = 39 - 7 - 14 - 14 = 4

white only = 62 - 27 - 14 - 14 = 7

let's place them in the appropriate sections on the diagram

Answer 5

that being said, it wants the # of dogs that have learned zero tricks, or in other words, no ribbons

the venn diagram only accounts for each dog once so it's simply

100 - all the #'s in the venn diagram

lmk if anything was confusing or if you'd like to check your solution