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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

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Q: How many blue counters must be added so that the ratio of yellow counters to total counters is 1 to 6?

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