There are black, purple and white counters in a bag in the ratio 14:20:7There are 39 more purple counters than white counters.How many black counters are there?

To solve this problem, we need to follow these steps:

1. First, we need to understand the ratio between black, purple, and white counters. The ratio is 14:20:7. This means for every 14 black counters, there are 20 purple counters and 7 white counters.

2. We know that there are 39 more purple counters than white counters. This difference corresponds to the difference in the ratio, which is 20 - 7 = 13.

3. Now, we can find out the equivalent of the ratio in actual numbers. If 13 in the ratio is equivalent to 39 in actual numbers, then 1 in the ratio is equivalent to 39 / 13 = 3 in actual numbers.

4. Finally, we can find out the number of black counters. If 1 in the ratio is equivalent to 3 in actual numbers, then 14 in the ratio (the number for black counters) is equivalent to 14 * 3 = 42 in actual numbers.

So, there are 42 black counters.