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.