Explanation:
Let's call the number of purple counters "x". This means that the number of blue counters is x - 78, and the number of white counters is 18x.
According to the ratio, the sum of the number of purple and blue counters is 16x + (x - 78) = 17x - 78.
And the sum of all counters is 16x + 18x + 3x = 37x.
Knowing that the sum of all counters is the same, we can set the two sums equal to each other:
37x = 17x - 78 + 37x
So, we have:
74x = 17x - 78 + 37x
57x = -78
x = -78/57
Since x can't be negative, we have to reject this solution.
However, the number of white counters can be found by multiplying 18 by the number of purple counters:
18 * x = 18 * (x/57) = (18/57) * x = (18/57) * 78 = 72
Therefore, there are 72 white counters in the bag.