Each barrel in the picture below contains either oil or vinegar.
The oil sells for twice as much as the vinegar.
Mr. P buys $28 worth of each, leaving one barrel.
Which barrel did he leave?
Solution to the Problem:
Mr. P bought the 13- and 15-gal barrels at $1.00 per gallon,
and he bought the 8-, 17-, and 31-gal barrels at 50 cents per gallon.
This left the 19-gal barrel which may contain either oil or vinegar.
Since Mr. P purchased the same dollar amount of vinegar and oil,
the number of gallons must be in a ratio of 2:1.
That means that the total number of gallons purchased must be divisble by 3.
If the 31-gal barrel were left, then the gallons purchased would be 72, which is divisible by 3.
However, the other 5 barrels can not add up to 24 and 48.
If the 19-gal barrel were left, then the gallons purchased would be 84, which is divisible by 3.
Since the other 5 barrels add up to 28 and 56, this is the answer.
If the 17-gal barrel were left, then the gallons purchased would be 86, which is NOT divisible by 3.
Therefore, this cannot be the answer.
If the 15-gal barrel were left, then the gallons purchased would be 88, which is NOT divisible by 3.
Therefore, this cannot be the answer.
If the 13-gal barrel were left, then the gallons purchased would be 90, which is divisible by 3.
However, the other 5 barrels can not add up to 30 and 60.
If the 8-gal barrel were left, then the gallons purchased would be 95, which is NOT divisible by 3.
Therefore, this cannot be the answer.