Jonathan has 1/3 as many green marbles as he has red marbles and 1/6 as many red marbles as he has yellow marbles.What part of his collection is made up of yellow marbles?

let the number of red marbles be x

number of green marbles = (1/3)x = x/3
yellow marbles = 6x

red : green : yellow = x : x/3 : 6x
= 3x : x : 18x

for a total of 24x

so yellows would be 18x/24x = 3/4 of his collection

1. 9/11

2. 1/6
3. 2/11
4. 3/22
5. 1/22

G= (1/3) R , R = (1/6 ) Y , Y = 6R

suppose total Marbels = G + R + Y = X
Part of Y = Y/X = Y/ (G + R + Y) = 6R / (R/3 + R + 6R)
= 18 R/ 22 R = 9/11

To determine the part of Jonathan's collection that is made up of yellow marbles, let's break down the ratios we have.

We are given that Jonathan has 1/3 as many green marbles as he has red marbles. Let's represent the number of red marbles as R. Therefore, the number of green marbles would be 1/3 * R.

We are also given that Jonathan has 1/6 as many red marbles as he has yellow marbles. Let's represent the number of yellow marbles as Y. Therefore, the number of red marbles would be 1/6 * Y.

Now that we have expressed the number of red and green marbles in terms of yellow marbles, we can find their relationship.

1/3 * R = 1/6 * Y

To solve for Y, we need to isolate it. Let's multiply both sides by 6 to clear the fractions:

6 * (1/3 * R) = 6 * (1/6 * Y)

2R = Y

This equation tells us that the number of yellow marbles (Y) is twice the number of red marbles (R).

Since we are looking for the part of the collection that is made up of yellow marbles, we need to calculate the ratio of yellow marbles to total marbles. Let's define the total number of marbles as T.

Y/T = Y / (R + 1/3 * R + Y)

We can substitute 2R for Y:

2R / T = 2R / (R + 1/3 * R + 2R)

Simplifying the denominator:

2R / T = 2R / (6/3 * R + 6/3 * R + 6/3 * 2R)

2R / T = 2R / (14/3 * R)

Canceling out the common factor of R:

2 / T = 2 / (14/3)

To divide by a fraction, we multiply by its reciprocal:

2 / T = 2 * (3/14)

Simplifying:

2 / T = 6/14

To find the part of the collection made up of yellow marbles, we can express it as a fraction:

Y/T = 6/14 = 3/7

Therefore, 3/7 of Jonathan's collection is made up of yellow marbles.