A jar of marbles is half red, one third green and the rest blue. If eight marbles are green how many are blue?

total --- x

red ---- x/2
green -- x/3
blue === y

y + x/2 + x/3 = x
y = x - x/2 - x/3
y = x/6

so one sixth are blue

To answer this question, we need to find the number of green marbles first. According to the information given, one-third of the jar is green. This means that the number of green marbles is equal to one-third of the total number of marbles in the jar.

Let's represent the total number of marbles as "x". Since one-third of the marbles are green, we can express this as (1/3)x.

Now, we are given that eight marbles are green. Therefore, (1/3)x = 8.

To solve for x, we need to isolate it. We can do this by multiplying both sides of the equation by 3:

(1/3)x * 3 = 8 * 3,

Simplifying:

x = 24.

So, there are 24 marbles in the jar.

Now, we need to find out how many of these marbles are blue. We know that half of the jar is red, and one-third is green. So, the remaining portion, which is blue, can be calculated by subtracting the sum of the red and green portions from the total number of marbles.

Blue marbles = Total marbles - Red marbles - Green marbles

Blue marbles = 24 - (1/2) * 24 - (1/3) * 24

Simplifying:

Blue marbles = 24 - 12 - 8

Blue marbles = 4.

Therefore, there are 4 blue marbles in the jar.