Box b contains ⅓ as many marbles as box a. box c contains ½ as many marbles as box b. the average number of marbles per box is 378. how many marbles are there in box b?

Answerthere are 252 marbles in box b.======let a represent marbles in box a, b represent  marbles in box b, c represent  marbles in box c."box b contains ⅓ as many marbles as box a" translated is:       b = 1/3 * a = a/3"box c contains ½ as many marbles as box b"    c = 1/2 * b = b/2but since b = a/3, we have    c = (b) / (2)    = (a/3) / (2)     = a/6"the average number of marbles per box is 378"since average value = (values) / (number of values), we have    378 = (a+b+c)/3    378 = 1/3 * (a+b+c)which sums the total number of marbles and divides by three because there are three boxes.since  b = a/3 and c = a/6, we have    a + b + c    = a + a/3 + a/6    = 6a/6 + 2a/6 + a/6 common denominator    = 9a/6    = 3a/2therefore    378 = 1/3 * (a+b+c)    378 = 1/3 * (3a/2)    378 = a/2    a = 756since b = a/3, we have b = 756/3 = 252there are 252 marbles in box b.in general, we would have 756 marbles in box a, 252 marbles in box b, and 126 marbles in box c. 

Im not that good with division but i think 5 is -6but dont quote me on thatim not the best in division but thats my answer