There are purple, green and black counters in a bag in the ratio 19:20:8There are 72 more green counters than black counters.How many black counters are there?

Step 1: Understand the ratio

The ratio of purple to green to black counters is 19:20:8. This means for every 19 purple counters, there are 20 green counters and 8 black counters.

Step 2: Understand the difference

The problem states that there are 72 more green counters than black counters.

Step 3: Calculate the ratio difference

The difference in the ratio between green and black counters is 20 - 8 = 12.

Step 4: Calculate the value of each ratio unit

If 12 units in the ratio is equivalent to 72 counters (from the problem statement), then 1 unit in the ratio is equivalent to 72 / 12 = 6 counters.

Step 5: Calculate the number of black counters

Since the ratio for black counters is 8, the number of black counters is 8 * 6 = 48 counters.