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?

Guest Jun 24, 2020

#1**+2 **

*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?*

Alan Jun 24, 2020

#2**0 **

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

ItzMe Jun 24, 2020