the number of elements in the union of the A sets is:5(30)−rAwhere r is the number of repeats.Likewise the number of elements in the B sets is:3n−rB
Each element in the union (in S) is repeated 10 times in A, which means if x was the real number of elements in A (not counting repeats) then 9 out of those 10 should be thrown away, or 9x.  Likewise on the B side, 8x of those elements should be thrown away. so now we have:150−9x=3n−8x⟺150−x=3n⟺50−x3=n
Now, to figure out what x is, we need to use the fact that the union of a group of sets contains every member of each set.  if every element in S is repeated 10 times, that means every element in the union of the A's is repeated 10 times.  This means that:150 /10=15is the number of elements in the the A's without repeats counted (same for the Bs as well).So now we have:50−15 /3=n⟺n=45
        
             
        
        
        
Answer:
D. Batch 5. 
Step-by-step explanation:
The batch should have the same proportion of blue to white to yellow. 
In Batch 1, there are two parts of blue, 1.5 parts of white, and 1 part of yellow. 
In Batch 5, there are four parts of blue, 3 parts of white, and 2 parts of yellow. 
4 / 2 = 2
3 / 2 = 1.5
2 / 2 = 1
Since the proportions are equal to those found in Batch 1, D. Batch 5 will create the same colors as the first batch. 
Hope this helps! 
 
        
             
        
        
        
Simply divide 61.50 by 3. You should be able to reach the answer that way
        
                    
             
        
        
        
Amount= Deposit or initial amount ( 1+ percent increase) ^period of time
So Amount= 50(1+0.1)^3
 = 50(1.1)^3
 = 50(1.331)
 =66.55
So she will have $66.55 in 3 years.