Question

There are purple, white and blue counters in a bag in the ratio 16:18:3

There are 78 more purple counters than blue counters.
How many white counters are there?

Answer 1

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.

Answer 2

Explanation: