Question

A collection of marbles has been divided into 3 different sets. The middle sized set is 2 times the size of the smallest set, and the largest set is 3 times as large as the middle-sized set. What fraction describes each part of the total marble collection

Answer 1

Answer:

Smallest set = $\frac{1}{9}$

Middle set = $\frac{2}{9}$

Largest set = $\frac{2}{3}$

Step-by-step explanation:

We are given the following in the question:

Marbles are divided into 3 groups.

Let x be the number of marbles in smallest group.

Then, according to the question:

Middle sized set = $2x\text{ marbles}$

Largest set =

$=3\times 2x\\=6x\text{ marbles}$

Fraction of marble in smallest set =

$=\dfrac{\text{Number of marble in the set}}{\text{Total number of marbles}} = \dfrac{x}{9x}\\\\=\dfrac{1}{9}$

Fraction of marble in middle sized set =

$=\dfrac{\text{Number of marble in the set}}{\text{Total number of marbles}} = \dfrac{2x}{9x}\\\\=\dfrac{2}{9}$

Fraction of marble in largest set =

$=\dfrac{\text{Number of marble in the set}}{\text{Total number of marbles}} = \dfrac{6x}{9x}\\\\=\dfrac{2}{3}$