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. 

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