Answer:
 13.  11 and 4
 14.  18 and 9
 15.  9 and 4
Step-by-step explanation:
You want the pairs of numbers that satisfy different relations:
 13. sum of 15, difference of 7
 14. ratio of 2:1, total of 27
 15. sum of 13, difference of 5
Consider the sum and difference problem:
 a + b = s . . . . . sum
 a - b = d . . . . . difference
Adding these two equations gives ...
 (a +b) +(a -b) = (s) +(d)
 2a = s +d
 a = (s +d)/2
Using the second equation to find b, we have ...
 b = a -d
The two numbers are ...
 (15 +7)/2 = 11
 11 -7 = 4
The two numbers are ...
 (13 +5)/2 = 9
 9 -5 = 4
When two numbers that total N have the ratio a : b, the first of them is ...
 a/(a+b) · N
and the second of them is ...
 b/(a+b) · N . . . . . . . also equal to N-a
The problem asks for two numbers that total 27 and have the ratio 2:1.
The larger is 2/(2+1)·27 = 18.
The smaller is 1/(2+1) ·27 = 9.
