Let the number of Yellow counters you already have is Y
Let the number of non-yellow counters you already have is Z
Then the current ratio of Yellow counters to the total counters
is Y : Y + Z
Let the number of Blue counters you add be B
After they have been added, the ratio of Yellow counters to the
total counters is Y : Y + Z + B
This is 1 : 6
Thus Y = 1
and Y + Z + B = 6
→ Z + B = 5
Which means that for the Yellow counters you have you will have
five times as many counters made up of whatever non-Yellow counters
you originally had plus the Blue counters you added.
Thus to find out how many Blue counters to add, take the number
of Yellow counters, multiply it by 5 and subtract the number of non
yellow counters you originally had.
examples:
You had 6 Yellow counters
Add 6 × 5 - 0 = 30 Blue counters
Which gives you 6 Yellow and 30 Blue counters
→ ratio Yellow : total counters = 6 : 30 + 6 = 6 : 36 = 1 :
6
You had 4 Yellow counters and 6 Red counters
Add 4 × 5 - 6 = 14 Blue counters
Which gives you 4 Yellow counters, 6 Red counters and 14 Blue
counters
→ ratio Yellow : total counters = 4 : 6 + 14 + 4 = 4 : 24 = 1 :
6
You had 4 Yellow Counters, 2 Blue counters and 3 Red
counters
Add 4 × 5 - (2 + 3) = 15 Blue counters
Which gives you 4 Yellow counters, 3 Red counters and 2 + 15 =
17 Blue counters
→ ratio Yellow : total counters = 4 : 3 + 17 + 4 = 4 : 24 = 1 :
6
