There are yellow and purple counters in a bag in the ratio 19:15There are 32 more yellow counters than purple counters.How many yellow counters are there?

Sure, let's solve this step by step:

1. We know that the ratio of yellow to purple counters is 19:15, which means for every 19 yellow counters, there are 15 purple counters.

2. We also know that there are 32 more yellow counters than purple counters.

3. Let's denote the number of '19 yellow counters' groups as x and the number of '15 purple counters' groups as y. So, we have 19x yellow counters and 15x purple counters.

4. According to the problem, 19x (yellow counters) is 32 more than 15x (purple counters). We can write this as an equation: 19x = 15x + 32.

5. To solve for x, we subtract 15x from both sides of the equation: 19x - 15x = 32, which simplifies to 4x = 32.

6. Then, we divide both sides of the equation by 4 to solve for x: x = 32 / 4, which gives us x = 8.

7. Now that we know x = 8, we can find the number of yellow counters by substituting x into the equation for yellow counters: 19x = 19*8 = 152.

So, there are 152 yellow counters.