Question 511349
Let 
Present age of Ashley =a
Present age of Mary =m

The ages of Ashley and Mary are in the ratio 4:7.
a:m=4:7
a/m=4/7
a=4m/7…………………….(1)
The sum of their ages is 22
a+m=22
a=22-m……………(2)
Put the value of a from (1) to (2)
a=22-m
4m/7=22-m
4m=7*(22-m)
4m=154-7m
4m+7m=154
11m=154
m=154/11
m=14
Put the value of m in (2)
a=22-m……………(2)
a=22-14
a=8
Present age of Ashley =a=8
Present age of Mary =m=14
Check
The ages of Ashley and Mary are in the ratio 4:7.
a:m=4:7
8:14=4:7
4:7=4:7
The sum of their ages is 22
a+m=22
8+14=22
22=22