The sum of two numbers is with a ratio of 15: 10. find the larger number.

Assume the sum is 100. The ratio of the two numbers is 15:10. This means that we can divide this indow 15+10, or 25 parts. Let us do that. Divide 100 into 25 parts and see how much is in each part. 100/25 is 4, meaning that there is 4 in each part. 15 parts will have 15*4, or 60. 10 parts will have 10*4, or 40. To confirm, add 40 and 60. It matches with what we started out with, 100. 

The two numbers, assuming the sum is 100, are 40 and 60. 60 is the greater value.