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You should consider 4 sub-sets of the total set of 200 bracelets:
- subset DR (have diamonds and rubies) of 50 elements (bracelets);
- subset DE (have diamonds and emeralds) of 70 elements (bracelets);
- subset ER (have emeralds and rubies) of 60 elements (bracelets);
- subset DER (have diamonds, emeralds and rubies) of 20 elements (bracelets).
How many bracelets have emeralds ?
To find it, we should add the numbers DE and ER and then subtract DER : DE + ER - DER = 70 + 60 - 20 = 110 (ANSWER).
Why we should add DE and ER, is clear to you without my explanations.
Why we should subtract DER ? - Because when we add DE and ER, we count DER twice.
How many bracelets have diamonds ?
To find it, we should add the numbers DR and DE and then subtract DER : DR + DE - DER = 50 + 70 - 20 = 100 (ANSWER).
Why we should add DR and DE, is clear to you without my explanations.
Why we should subtract DER? - Because when we add DR and DE, we count DER twice.
How many bracelets have rubies ?>
Use the same logic and complete the solution on your own.
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See the lesson
- Counting elements in sub-sets of a given finite set
in this site.
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comment from student: This is wrong. The total number of bracelets is suppose to equal 200 and this equals 300
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My response :
My solution and my answers are correct !
Your comment is WRONG.
Why ? - Because when you add the numbers, you count many bracelets twice and even thrice !
Your tone/comment is very aggressive. (Too aggressive to be polite . . . )
Please do not forget that you talk with the EXPERT.