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
