Question 502348
Let 
Present age of Chloe = c
Present age of Danny = d

Given
Five years ago means we have to subtract 5 from their present age
c-5=d-5
then
Chloe was twice as old as Danny
(c-5)=2(d-5)
c-5=2d-10
c=2d-10+5
c=2d-5...............(1)
Seven years hence means we have to add 6 in their present age
c+7=d+7
then
Three times Chloe's age will be four times Danny's age
3(c+7)=4(d+7)
3c+21=4d+28
3c=4d+28-21
3c=4d+7..............(2)
Put the value of c from (1) to (2)
3c=4d+7
3(2d-5)=4d+7
6d-15=4d+7
6d=4d+7+15
6d-4d=22
2d=22
divide by 2 both sides of the above equation
2d/2=22/2
d=11
Put the value of d in (1)
c=2d-5...............(1)
c=2(11)-5
c=22-5
c=17

Present age of Chloe = c = 17 years
Present age of Danny = d = 11 years