There are 396 marbles in a bag. The bag contains red, yellow, and purple marbles. If the ratio of red to yellow marbles is 2:3 and the ratio of yellow to purple marbles is 1:2, how many yellow marbles are in the bag?

The no. of Red, Yellow and Purple marbles are 72, 108, 216 respectively.

Step-by-step explanation:

Let us consider the no. of red marbles be R

Let the no. of yellow marbles be Y

Let the no. of purple marbles be P

Given that there are 396 marbles in the bag.

Total marbles = R+ Y + P

   396 = R + Y + P

The ratios are given as below:

   R : Y =2/3

Which means,  R/Y = 2/3

       R= 2Y/3

       Y: P = 1/2

Which means, Y/P = 1/2

       1/P = 1/2Y

         P = 2Y

Here we got the values of P and R in terms of Y.

Total marbles = R + Y + P

   396 =( 2Y/3) +Y+(2Y)

Taking LCM, we have 3 as LCM

   396 = (2Y +3Y+ 6Y) / 3

   396 x 3 = 2Y + 3Y + 6Y

   1188 = 11Y

   11Y = 1188

   Y = 1188/11

   Y = 108

R/Y = 2/3

R/108 = 2/3

R = 2(108) /3

R= 72

Y/P = 1/2

108/ P = 1/2

1/P = 1/2(108)

P = 2(108)

P = 216

The no. of Red, Yellow and Purple marbles are 72, 108, 216 respectively.

so, converting firstly the mixed fractions to improper fractions and then "adding".