SOLUTION: Mrs Smith bought 6 buckets of wine, A, B, C, D, E and F. Their capacities were 5L, 6L, 8L, 9L, 10L and 11L respectively. She kept one bucket of wine for herself and sold the rest t

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Question 983556: Mrs Smith bought 6 buckets of wine, A, B, C, D, E and F. Their capacities were 5L, 6L, 8L, 9L, 10L and 11L respectively. She kept one bucket of wine for herself and sold the rest to Mrs Bread and Mrs Regan. Which buckets Mrs Smith keep for herself if Mrs Bread bought twice as many litres as Mrs Regan?
Answer by KMST(5328) About Me  (Show Source):
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I see only one answer that makes sense.
p= the capacity (in L) of the one bucket Mrs Smith kept for herself.
n= the sum of the capacities (in L) of the buckets Mrs Smith sold to Mrs Regan.
2n= the sum of the capacities (in L) of the buckets Mrs Smith sold to Mrs Bread.
2n%2Bn=3n= the sum of the capacities (in L) of the buckets Mrs Smith sold to Mrs Bread and Mrs Regan.
3n%2Bp= the sum of the capacities (in L) of all the buckets Mrs Smith had before selling any.
Since the sum of the capacities (in L) of all the buckets Mrs Smith had before selling any is
5L%2B6L%2B8L%2B9L%2B10L%2B11L=49L ,
3n%2Bp=49
3n%2Bp=3%2A16%2B1
p=3%2A16-3n%2B1
p=3%2A%2816-n%29%2B1
16-n%29%29%29+is+a+whole+number%2C+meaning+that+%7B%7B%7B3%2A%2816-n%29 is a multiple of 3 ,
so p must be 1 more than a multiple of 3 .
3%2B2=5 , 6=2%2A3 , 9=3%2A3 and 11=9%2B2=3%2A3%2B2 do not work.
3%2B1=4 , 6%2B1=7 and 12%2B1=13 would work too, but are not options.
highlight%28p=10%29 works because 9%2B1=10 .
That would make 3n%2B10=49-->3n=39-->n=13 ,
and since 8%2B5=13 , Mrs Regan must have bought the 5L and 8L buckets,
and Mrs Bread must have bought the remaining 3 buckets:
6L%2B9L%2B11L=26L=2%2A%2813L%29 .