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Set A has 10 more elements than set B. The two sets have 7 elements in common, and the total number of unique elements across both sets is 85.  How many elements set A have?

 Jun 24, 2020
 #1
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Set A has 10 more elements than set B. The two sets have 7 elements in common, and the total number of unique elements across both sets is 85.  How many elements set A have?

 

 Jun 24, 2020
 #2
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The number of elements in set A I called A, and the number of elements in sent B I called B. So, image that its a venn diagram, in the middle part, there would be 7 numbers. But when it says that "the total number of unique elements across both sets is 85", we can write it as 85=(A-7)+(B-7), beacuse it says that it excludes the middle part. so if we simplify that we get 85=A+B-14, which we can further simplify to 99=A+B. Later on it says that "Set A has 10 more elements than set B" so we can write that as A=B+10, or B=A-10, whitch would be easier in our case. So from there we can substetute to get 99=A+A-10, from 109=2A, and A=54.5. 

 

I hope you found this helpfull

 Jun 24, 2020

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