A bag contains marbles of three different colours. 1/5 of the marbles are blue. The ratio of the number of pink marbles to that of orange marbles is 2:3. What is the ratio of the number of blue marbles to that of orange marbles?

Answer 1

total ---- 5x
blues --- x , defined this way to avoid as many fractions as possible
rest of marbles : 5x-x = 4x <------ pinks and orange marblesx :

pink : orange = 2:3 = 2k : 3k

then 4x = 5k
k = 4x/5

ration of blue : orange = x : 3k
= x : 3(4x/5)
= 1 : 12/5
= 5 : 12

check: suppose there are 1200 marbles
1/5 or 240 would be blue, then the remaining 960 would be
pink and orange in the ration of 2:3, or
384 pink and 576 orange , (note 384:576 = 2:3)
ratio of blue to orange = 240 : 576 = 5:12