One-third of the dairy cattle on a farm are in the barn. Three-fifths of the beef cattle are in the barn. There are 30 dairy cattle and 15 beef cattle in thr barn. How many more dairy cattle are on the farm than beef cattle?

Let

d = the total number of dairy cattle

b = the total number of beef cattle

2/3 of the dairy cattle on a farm are in the barn, and we know that 24 dairy cattle are in the barn thus:

(2/3) d = 24

d = 36 dairy cattle

1/4 of the beef cattle are in the barn and there are 16 beef cattle in the barn thus:

(1/4) b = 16

b = 64 beef cattle

64 - 36 = 28

There are 28 more beef cattle on the farm than dairy cattle.