summerbunni05
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please help me with this question and provide work

Vatruvious purchased what he thought were 6 barrels of soda, only to find out that one of the barrels contained apple juice. (He loved apple juice!) The barrels held 15 liters, 19 liters, 20 liters, 16 liters, 31 liters, and 18 liters. He sold some of the barrels to Emmett and some to Lucy. Emmett purchased twice as many liters as Lucy did. Being very fond of apple juice Vatruvious kept this barrel for himself. Which barrel (in liters) contained the apple juice? Of course, Vatruvious sold the barrels as he bought them, without taking a drink from any of the barrels, so tasting didn't help him figure this one out. Also, which barrels did Emmett purchase and which did Lucy purchase?

15 L
19 L
20 L
16 L
31 L
18 L

answer choices: Lucy, Vatruvious kept this one, Emmett ​

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sqdancefan

Answer:

  Lucy: 15 L, 18 L

  Emmett: 16 L, 19 L, 31 L

  Vatruvious: 20 L

Step-by-step explanation:

The total number of liters purchased by Lucy and Emmett must be divisible by 3. The total number of liters Vatruvious bought is ...

  15 +19 +20 +16 +31 +18 = 119

This number has a remainder of 2 when it is divided by 3. That means the number of liters Vitruvious kept must have a remainder of 2 when divided by 3.

  15/3 = 5 r 0

  16/3 = 5 r 1

  18/3 = 6 r 0

  19/3 = 6 r 1

  20/3 = 6 r 2 . . . . the barrel Vitruvious kept

  31/3 = 10 r 1

The barrels Vitruvious sold total 119 -20 = 99 L, so Lucy bought 99/3 = 33 liters and Emmett bought 99 -33 = 66 liters.

The above remainders suggest that the sales were as follows:

  Lucy bought 15 L + 18 L = 33 L

  Emmett bought 16 L +19 L + 31 L = 66 L

  Vitruvious kept 20 L

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