There are red and blue marbles in a jar one-third of the marbles are red if another marble is added to the jar then 3 8 of the marbles will be red how many marbles are blue?

Answer 1

Depends on what the question is actually saying:

If the "3 8" is 38 (thirty eight):

Let R = number of red marbles to begin with.

Let B = number of blue marbles

Given two facts:

R = (1/3)(R+B)

R+1 = 38. (This assumes it's a red marble added)

2nd equation gives R = 37

1st equation gives B = 2R = 2*37 = 74 blue

If the "3 8" is 3 over 8 (3/8 or three eighths):

If a non-red marble is added, the problem is unsolvable as 3/8 is greater than 1/3, but with more marbles and the same number of red marbles, the fraction of red marbles will be less than 1/3. Thus it is assumed that a red marble is added:

Let M be the number of marbles in the jar, and R be the number of red ones, then:

1/3 M = R -- one third are red

3/8 (M + 1) = R + 1 -- when an extra red marble is added, 3/8 of the marbles are now red marbles

Substituting R from the first equation into the second equation gives and solving gives:

3/8 (M + 1) = 1/3 M + 1

→ 9/8 (M + 1) = M + 3

→ 9(M + 1) = 8M + 24

→ 9M + 9 = 8M + 24

→ 9M = 8M + 15

→ M = 15

1/3 are red → 2/3 are blue

→ 2/3 x 15 = 10 are blue

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Another Answer:

1/3+1/24 = 3/8 It doesn't how many red marbles are added because now there are 24 but before there were 23 which is 1/3 of 69 of which 2/3 are 46 blue marbles.