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# Help

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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  dogs in the school.

62 have blue ribbons, 55 have green ribbons, and 63 have white ribbons.

32 have a blue ribbon and a green ribbon; 31 have a green ribbon and a white ribbon; 39 have a blue ribbon and a white ribbon.

16 have all three ribbons.

How many dogs have not learned any tricks?

Jan 29, 2020

#1
+18875
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16 have all three ribbons.

Because 32 have a blue ribbon and a green ribbon and 16 have all three ribbons,

32 - 16  =  16 have blue and green ribbons only (no white ribbon).

Because 31 have green and white ribbons and 16 have all three ribbons,

31 - 16  =  15 have green and white ribbons only.

Because 39 have blue and white ribbons and 16 have all three ribbons,

39 - 16  =  23 have blue and white ribbons only..

Since 62 have blue ribbons, subtracting those that have all three ribbons (16) and those that also have a green ribbon (16) and those that also have a white ribbon (23), we are left with 7 that have only a blue ribbon.

You can work in a similar fashion to determine how many only have a green ribbon and how many have only a white ribbon.

Finally, subtract all these non-overlapping groups to find out how many have no ribbons at all.

Jan 29, 2020
#2
+21931
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