a vendor has six jugs of punch with capacities of 13, 15, 16, 21, 21, and 22 gallons. one jug, which he keeps for himself, is full of blue punch. the other five jugs are full of red punch. without opening any of the jugs, he sells 1/3 of the red punch to randy and the remaining 2/3 of the red punch to lisa. how many gallons of the blue punch did he keep for himself?

Answer:Possible capacity of Blue punch jug = 21 gallonsStep-by-step explanation:In the question,Total number of jugs = 6Capacities of jugs = 13, 15, 16, 21, 21, 22Total capacity of all the jugs = 108 gallonsOne of the jug is filled with Blue Punch.Other remaining Five Jugs, with Red punch.As,He distributed the Red Punch in 2 parts of 1/3 and 2/3.1/3 to Randy and 2/3 to Lisa.So,There are only two possibilities for which he can have the Blue jug Punch all to himself of the capacity,Possibility 1 :Blue Punch = 15 gallonsRed Punch = 108 - 15 = 93 gallonsNow, one third will be 31 gallons which is not a possible portion without opening the jugs.Therefore, the 15 gallons of Blue Punch can not be a case.Possibility 2 :Blue Punch = 21 gallonsRed Punch = 108 - 21 = 87 gallonsOne-third will be = 29 gallons which can be a possible combination of 13 and 16 gallons jug.Therefore, the Blue punch Jug will be of 21 gallons capacity.